Find f'(x)

f (x) = 2e
5x

f'(x) = 2e^(5x) * 5

To find the derivative of f(x) = 2e^(5x), we can use the chain rule. The chain rule states that if we have a function of the form g(h(x)), then the derivative is g'(h(x)) times h'(x).

In this case, g(u) = 2e^u and h(x) = 5x.
First, we find the derivative of g(u) with respect to u (which is the derivative of e^u):
g'(u) = e^u.

Next, we find the derivative of h(x) with respect to x:
h'(x) = 5.

Now, we can apply the chain rule:
f'(x) = g'(h(x)) * h'(x)
= e^(5x) * 5
= 5e^(5x).

Therefore, f'(x) = 5e^(5x).