Question

Let f(x) = 5e^x + e^4.
f'(x) = ?

Answer 1

To find the derivative f'(x) of the function f(x) = 5e^x + e^4, apply differentiation rules: f'(x) = 5e^x, since the derivative of a constant is 0.

Step-by-step explanation:

The student has asked for the derivative of the function f(x) = 5e^x + e^4. To find f'(x), we need to apply the rules of differentiation to f(x). The derivative of 5e^x is 5e^x since the derivative of e^x with respect to x is e^x and we multiply that by the constant coefficient (5). The derivative of e^4 is 0 since e^4 is a constant and the derivative of any constant is 0. Therefore, f'(x) = 5e^x.