If f(x) = e^x * sin(x), what is f'(x)?

D. B) e^x * sin(x) + e^x * cos(x)

If f(x) = e^x * sin(x), what is f'(x)?

D. B) e^x * sin(x) + e^x * cos(x)

AP Calculus ABeasymcq1 pt

If f(x) = eˣ * sin(x), what is f'(x)?

A.C) eˣ * cos(x) - eˣ * sin(x)

B.D) eˣ * sin(x) - eˣ * cos(x)

C.A) eˣ * cos(x)

D.B) eˣ * sin(x) + eˣ * cos(x)

Explanation

Core Concept

This function is a product of two functions, so we need to use the product rule: (fg)' = f'g + fg'. Let f(x) = eˣ and g(x) = sin(x). Then f'(x) = eˣ and g'(x) = cos(x). Applying the product rule: f'(x) = eˣ * sin(x) + eˣ * cos(x) = eˣ(sin(x) + cos(x)). Therefore, the correct answer is B.

Correct Answer

DB) eˣ * sin(x) + eˣ * cos(x)

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