Let f be the function given by f(x) = 2 cos x + 3ex. What is the value of f'(0)?

Question

Let f be the function given by f(x) = 2 cos x + 3e^x. What is the value of f'(0)?

A) 3

B) 5

C) 8

D) 11

Answer 1

You should have learned that 1) the derivative of two functions that are added together is just the derivative of each added together, 2) the derivative of a constant times a function is just that constant times the derivative of the function, 3) that the derivative of cos(x) is -sin(x) and 4) that the derivative of e^x is e^x so:

For f(x) = 2cos(x) + 3e^x

f '(x) = -2sin(x) + 3e^x

So f '(0) = -2sin(0) + 3e⁰ = -2(0) + 3(1) = 3