Take a multiple choice test on derivatives.
Table of contents
In this test you will be asked questions about the following topics:
Derivatives of trigonometric functions
When you give a right answer, it is marked with .
When you give a wrong answer, it is marked with and the right answer is marked with .
When you answer a question, your score is updated and you can read an explanation of the right answer before going to the next question.
Are you ready?
Question 1. DefineThe derivative of is:
Explanation. The function is a composite function:where:andWe need to use the chain rule for the derivative of a composite function:The derivative of is:The derivative of is:which evaluated at gives:Therefore:See the calculus review page entitled Derivatives - Review for more details.
Question 2. DefineThe derivative of is:
Explanation. We need to use the rule for differentiating a product of functions:See the calculus review page entitled Derivatives - Review for more details.
Question 3. DefineThe derivative of is:
Explanation. The function is a composite function:where:andWe need to use the chain rule for the derivative of a composite function:The derivative of is:The derivative of is:which evaluated at gives:Therefore:See the calculus review page entitled Derivatives - Review for more details.
Question 4. DefineThe derivative of is:
Explanation. The function is a trigonometric function multiplied by a constant ():See the calculus review page entitled Derivatives - Review for more details.
Question 5. DefineThe derivative of is:
Explanation. We need to use the rule for differentiating a product of functions:See the calculus review page entitled Derivatives - Review for more details.
Question 6. DefineThe derivative of is:
Explanation. The function is a composite function:where:andWe need to use the chain rule for the derivative of a composite function:The derivative of is:The derivative of is:which evaluated at gives:Therefore:See the calculus review page entitled Derivatives - Review for more details.
Question 7. The functionis the derivative of:
Explanation. The function is a trigonometric function () multiplied by a constant (). Its derivative is:See the calculus review page entitled Derivatives - Review for more details.
Question 8. The function:is the derivative of:
Explanation. The function is a composite function:where:andWe need to use the chain rule for the derivative of a composite function:The derivative of is:The derivative of is:which evaluated at gives:Therefore:See the calculus review page entitled Derivatives - Review for more details.
Question 9. The function:is the derivative of:
Explanation. We need to use the rule for differentiating a linear combination of functions:See the calculus review page entitled Derivatives - Review for more details.
Question 10. The function:is the derivative of:
Explanation. The function is a composite function:where:andWe need to use the chain rule for the derivative of a composite function:The derivative of is:The derivative of is:which evaluated at gives:Therefore:See the calculus review page entitled Derivatives - Review for more details.
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