Question

Find the function whose derivative is f'(x) = e^{5x} :

a) 1/5e^{5x} + C
b) e^{5x} + C
c) 1/5e^{5x^2} + C
d) 5e^{x} + C

Answer 1

The function whose derivative is f'(x) = e^{5x} is given by option (a) 1/5e^{5x} + C.

Step-by-step explanation:

The function whose derivative is f'(x) = e^{5x} is given by option (b) e^{5x} + C.

To find the original function, we need to integrate f'(x) with respect to x. Integrate e^{5x} with respect to x to get:

f(x) = 1/5e^{5x} + C

where C is the constant of integration. Therefore, the answer is option

(a) 1/5e^{5x} + C