### Chapter 3 Test, Question #1

Differentiate:

Here we must first recognize that we are dealing with the product rule, meaning that we must multiply the derivative of the outside function by the inside function and then add the outside function times the derivative of the inside function. So:

Derivative of is by the derivative of exponential rule.

Derivative of is by the definitions of trigonometric derivatives.

Therefore by putting the information we have into the product rule, we get:

which, rearranged, looks just like answer (c) which is:

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