Create a function where you must use the product rule, quotient rule, and chain rule one time each to differentiate it. State the order in which you would take derivative by indicating which rule is used first, second, and last. Your example must contain a trigonometric function and a logarithmic function within it.

For this assignment, you will be applying your knowledge of derivative rules by creating a function that requires product, quotient, and chain rule when taking derivative. The second part of the assignment you have an opportunity to earn some extra credit towards your class engagement portion of your grade. Part I is the assignment and Part II is extra credit that you may choose to complete or not to complete. 😊

Part I:

Create a function where you must use the product rule, quotient rule, and chain rule one time each to differentiate it. State the order in which you would take derivative by indicating which rule is used first, second, and last. Your example must contain a trigonometric function and a logarithmic function within it.

Example: y equals cos open parentheses fraction numerator x e to the power of x over denominator 4 x cubed minus 5 x plus 1 end fraction close parentheses would be chain rule first, then quotient rule, then product rule to differentiate it.

Next, take the derivative of the function you created.

Part II:

Refer to the following Derivative Rules Examples Handout Actions.
For each function, determine if the derivative is correct or incorrect.
Note that a derivative may be correct even if it is not stated in simplified form.
Write the question letter on your paper. If the derivative is correct, state “correct”. If the derivative is incorrect, state “incorrect.”

Submission Requirements:

Clearly label Part I and Part II on your paper.
Organize your work in order for each part.
Combine into a single PDF file and submit.

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