AP Calculus ABeasymcq1 pt
If f(x) = e^x * sin(x), what is f'(x)?
A.C) e^x * cos(x) - e^x * sin(x)
B.D) e^x * sin(x) - e^x * cos(x)
C.A) e^x * cos(x)
D.B) e^x * sin(x) + e^x * 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) = e^x and g(x) = sin(x). Then f'(x) = e^x and g'(x) = cos(x). Applying the product rule: f'(x) = e^x * sin(x) + e^x * cos(x) = e^x(sin(x) + cos(x)). Therefore, the correct answer is B.
Correct Answer
DB) e^x * sin(x) + e^x * cos(x)
Practice more AP Calculus AB questions with AI-powered explanations
Practice Unit 1: Limits and Continuity Questions →