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.
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