This resource contains total of 32 problems. Students will practice differentiation of common functions using the product and quotient rules ( they don’t need to apply the chain rule). The packet has 3 worksheets: ⟐ The first worksheet has the students finding the first derivatives of 16 functions using the differentiation formulas and product rule. ⟐ The second worksheet is finding the first derivatives of 10 functions using using the differentiation formulas and quotient rule. ⟐ The third worksheet is finding the first derivatives of 6 functions using the combination of the product and quotient rules. It contains more complicated problems. These six challenging problems are suitable for advanced calculus students. The worksheets can be used as class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be also used as a partner activity like this: ⟡ Partner A will solve WS #1 while Partner B solves WS #2, then they swap papers and Partner A will solve WS #2 while Partner B solves WS #1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Then partners solve the problems of WS#3 collaborating or each partner may solve half of the WS #3 problems.

This activity practices finding derivatives (a total of 12 various examples) using the chain rule. Functions include polynomials, radicals, trig and inverse trig functions, exponential functions and natural logarithms. Activity Directions: Students have to compute 12 derivatives. They are asked to use a table given to find the mathematician’s name corresponding to each of their answers. (To facilitate students all the answers correct and incorrect are labeled with big Latin letters and are contained in another table.) If students find all the derivatives correctly, they will learn 12 names of mathematicians involved in calculus. This activity can be used as a class practice. (Students could compete to see who can get all or most names first). It can be also used for groups of 2 (each partner will solve 6 problems) or independent activity. Solutions (handwritten clearly) to the problems are provided.

This resource contains 20 practice problems (20 functions given) for classifying critical points of a function. Functions included are polynomials, rational, including radicals (square and higher-index roots), exponential, logarithmic, trigonometric and inverse trigonometric. To solve each problem students will need to find critical numbers determine the intervals on which the function increases and decreases apply the First Derivative Test to classify the critical points as relative maximums, relative minimums or neither (locate relative extrema of a function). The product can be used as in class practice, an independent practice, partner activity, for group work, as enrichment. Detailed and typed answer keys are provided.

This is a collaborative and challenging activity to practice finding first and second derivatives of simple and composite functions. The functions in this activity include polynomials, rational fractions, radicals, trig and inverse trig expressions, exponential expressions and natural logarithmic functions. Students work through 14 sections/problems(or less if preferred). Each section contains one function to be differentiated by the partners. One partner starts solving first to find the first derivative of the function, then the other partner differentiates the function that his partner has obtained to find the second derivative. In the next section, partners take turns and it goes the same way. Alternative way to use this activity: Partners can work over finding the first derivatives of the functions of two randomly chosen different sections and then to swap papers to find the second derivative of the same functions. A hint is provided in each section that gives the sum of the partners’ answers. Typed and detailed answer keys are included. I hope this activity will be stimulating and beneficial for your calculus students.

In this fun ghosts themed activity, students will practice finding a derivative at a point. The problems covers all the basic derivative rules, including power rule, product and quotient rules, chain rule, polynomial, rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic functions. Activity Directions: Student work through 12 problems (functions given). They choose a function to find the value of its first derivative at the given value of x. The solutions of all problems are written on twelve of 13 ghosts on a given picture. Every time students arrive at a correct answer, they will “cast out the ghost” having this answer written on it. Students are also asked to find the only one ghost who can NOT be cast out. The product can possibly be used as a partner or a group activity(group of 3). Student recording sheets are provided and an answer key.

This fun Thanksgiving themed activity will help students review such topics as ♦ first, second and higher order derivatives ♦ intervals of increasing and decreasing ♦ critical points and local extrema The functions included are polynomial, rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic (common and composite functions). The problems covers all the basic derivative rules, including power rule, product and quotient rules and chain rule. Activity Directions: Students work through 15 problems. All the answers are written on 15 of 18 turkeys on a given picture. Every time students arrive at a correct answer, they will “get the turkey” having this answer written on it. Students are asked to find three happy turkeys who can NOT be caught. The product can be possibly used as a partner or a group activity (group of 3). Student recording sheets and the answer key are provided. I wish you very happy and blessed Thanksgiving!

Students will practice the chain rule with this fun multiple-choice game. On each page/slide there are given a picture of a horse, a function that students have to differentiate and four answer choices. Name of horse breed corresponds to each answer choice. Students solve the problem and choosing an answer they find out what horse breed is this one on the picture. The problem pages/slides are 12. The functions included are polynomial, rational, radical, exponential, logarithmic, trigonometric and inverse trigonometric. Answer key is included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here. I have included 2 PDF files - the one has each slide as a page and the other has three slides on a page for easy and more economic printing!

This activity practices finding 16 derivatives using the chain rule. Composite functions include polynomials, rational fractions, radicals, trig and inverse trig expressions, exponential expressions and natural logarithmic functions. Students have to solve 8 complicated problems - examples of 8 functions where each function is expressed as the sum of two composite functions. Students will need to use linear combination rule to find the derivatives of these 8 functions. Thus, they will solve coupled problems consisting of two sub – problems (practice 2 in 1) in three steps. This can be used as a class practice/independent practice in 2 steps or as a partner activity (Partner A will find the derivative of one addend of the function while Partner B computes the derivative of the other addend, then partners will sum their derivatives to find the answer of the problem). These worksheets can be also used for enrichment or homework. Typed solutions to problems are provided.

This is an engaging activity on the chain rule. On each page/slide students are given the solution of one problem and another similar problem to the first one to try to solve it by their own. Each problem consists of two sub problems - a) problem which is finding the first derivative and b) problem - computing the first derivative at a point (for a given value of the variable x). There are given the solutions of 8 problems and 8 similar to them problems for independent work. Functions included are composition of polynomial, rational, radical,exponential, logarithmic, trigonometric and inverse trigonometric functions. The last three problems are more challenging - students have to find the first derivative of a function of the type f(g(h(x))) using first the power rule for the function f. The product can be used after teaching a lesson on the chain rule, as an independent/extra practice and homework assignment. Answer keys are included. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here. I have included 2 PDF files - the one has each slide as a page and the other has two or three slides on a page for easy and more economic printing!

This is a challenging activity created for students to improve their calculus skills with more complicated examples on differentiation using the chain rule. The functions in this activity include polynomials, rational fractions, radicals, trig and inverse trig expressions, exponential expressions and natural logarithmic functions. Students have to differentiate 8 composite functions and show all their work. They аrе given the answer to each problem with missing coefficients. Students are asked to find these coefficients and fill in the corresponding empty squares for the answer. This resource can be used for class work, independent practice or partner activity, for enrichment and homework assignment. Full typed solutions to the problems are provided.

This activity practices finding derivatives using the chain rule. The composite functions include rational, radical, trigonometric and inverse trigonometric, exponential and logarithmic functions. The most of the problems are challenging for students to improve their skills on differentiation using the chain rule. There are 12 black kitten - themed task cards each containing 2 tasks. On each card is given a function. Students are asked to find the first derivative (1 task) compute the first derivative at a given point (2 task) Students can use the cards working individually or in groups of 2, 3 and/or 4. Student recording sheets and typed answer keys are included.

This is a pumpkin themed activity on composition of functions and THE CHAIN RULE. There are given two functions f(x) and g(x) and problems 1 and 2 on each page/slide. Problem 1 asks to be found the function F(x)=f(g(x)) and its first derivative and problem 2 asks to be found the function G(x)=g(f(x)) and the first derivative of it. Partner A can solve the problem 1 and partner B can solve the problem 2 if you decide to use this activity as a partner activity. The problems are challenging. Partners have an opportunity to collaborate and compare their results. The problem slides are six and the answer key slides are three. NOTE: This product is created as a Google Slides product. I have converted it to PDF item here. I have included 2 PDF files - the one has each slide as a page and the other has three slides on a page for easy and more economic printing!

This is a collaborative and challenging activity for classifying critical points of a function using the first and second derivative tests. The functions in this activity include polynomials, rational fractions, radicals, exponential and natural logarithmic expressions, trig and inverse trig expressions. Partners work through 12 sections/problems (functions given). Partner A will use the First Derivative Test to find the local extrema for the given function while Partner B uses the Second Derivative Test to find the local extrema for the same function. Then partners compare their results. In the next section, Partner A will use the Second Derivative Test and Partner B will use the First Test to locate all the relative extrema. Partners compare their answers again. Detailed typed answer keys are provided.

This is a self-checking practice created for students to find the first and second derivatives of common and composite functions. The functions include polynomials, rational fractions, radicals, trig and inverse trig expressions, exponential expressions and natural logarithmic functions. In each section, students have to differentiate once or twice a function given and then to prove that this function satisfies a given differential equation. Thus, students check whether they have computed the derivatives correctly. (There are sections 12 in total - 12 functions and 12 differential equations). The resource can be used for class work, independent practice or partner activity, for enrichment and homework assignment. Typed solutions to the problems are provided.

This resource contains total of 50 problems. Students will practice differentiation using the basic properties of derivatives and the power rule only. The packet has 6 worksheets: ⟐ The first and second worksheets WS # 1A and WS # 1B are similar. Students will have to find the first derivatives of 10 various functions ( polynomial, rational and radical). These are designed to be possibly used as a partner activity. ⟐ The third worksheet is finding the first derivatives of 10 functions as some of the examples are a bit more complicated and challenging than WS # 1A and WS #1B problems. ⟐ The fourth worksheet is finding the second derivatives of 8 various functions ( polynomial, rational and radical). ⟐ The fifth worksheet has the students finding the equation of the tangent line for 6 given functions at indicated points. ⟐ The sixth worksheet asks the students to determine the intervals on which 6 given functions are increasing and decreasing. The worksheets can be used as class practice, for an extra practice or enrichment, an assessment or homework assignment. It can be used as a partner activity – for instance: ⟡ Partner A will solve WS # 1A while Partner B solves WS # 1B, then they swap papers and Partner A will solve WS # 1B while Partner B solves WS # 1A. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. Answer keys are NOT included!

This resource contains total of 20 problems. Students will practice differentiation using the chain rule. The composite functions include polynomials, rational, radicals, trig and inverse trig, exponential and logarithmic expressions. The packet has 2 worksheets of 10 derivative problems. The worksheets can be possibly used as two different forms for partner activity like that: ⟡ Partner A will solve WS # 1 while Partner B solves WS # 2, then they swap papers and Partner A will solve WS # 2 while Partner B solves WS # 1. Once they have completed the work, they compare their results. If there are different answers to one and the same problem, students have to identify and correct any errors. The worksheets can be also used for an extra practice or enrichment, an assessment or homework assignment. If you download this product, please take a moment to leave your comments. I LOVE hearing from you ❣❣❣

This is a collaborative activity to practice evaluating indefinite integrals by using Integration by Parts. It aims to develop and consolidate student’s skills in both integration and differentiation as well. Partners work through 16 sections (or less if preferred) each containing one integral. Activity Directions: A partner start solving an integral while the other partner is waiting for the answer to check it by differentiating. In the next section, partners take turns and it goes the same way. An alternative (saving time) way to use this activity: Partner A solves an integral of a section while Partner B solves an integral of the other (the next in line) section. Then they swap papers and differentiate the obtained functions to check each other’s answers. A purpose of this activity is to aid learners gain a better understanding of integration. I hope it will be helpful for your calculus students. Typed answer keys are included

In this engaging and self-checking activity students will practice integration of trig functions using the following trig substitutions: ▸ t = tan(x/2) ▸ t = sinx or t = cosx ▸ t = tanx There are 12 task cards – recording sheets with space provided for students to show their work. Students have 4 indefinite integrals for each type trig substitution. They are instructed which one trig substitution(s) to apply so to solve the problems easily. After finding the integral, students must fill in the missing function f(x) in a corresponding empty rectangle for the answer given coded at the bottom of the worksheet card. The product can be used as an independent practice or for class work to organize students in cooperative learning groups. It is also great for extra integration practice or enrichment. Answer keys are included. Typed solutions to problems A, D, E and H are provided to be possibly used as a guide. NOTE: There are also included worksheet cards with only the problems given (without answers) so the cards can be used as worksheets, homework assignment and even as an assessment.

This activity is created for your students to practice their skills with more complicated trig integrals. It contains problems on indefinite integrals of product and ratio of sine and cosine involving powers of sine and cosine. In general, the integrals are of (sin(x))^n(cos(x))^m, where m and n are integers. Students will need to use trigonometric identities (Pythagorean, Power Reduction Identities, Double-Angle Identities), integration by u-substitution, integration by parts along with algebra skills to manipulate the integrands. There are 16 problems for them to complete with room to show work. Students аrе given the answer to each problem with missing coefficients they have to find and insert/fill in. This resource can be used for class work, independent or grouped, HW, enrichment, or an assessment. Answer keys are included.