You have to apply what is known as the Chain Rule in the case of e^4x. The Chain rule is f(g(x))' = f'(g(x)) * g'(x). f'(x) = e^x , g(x) = 4x, g'(x) = 4
(e^4x)' = e^4x * 4 = 4e^4x
Another (easier) way to write the chain rule is . So you let your "inner" function of x be u, so that you can then write your function y in terms of u, take the derivative of each, then convert back to a multiple of x and multiply them.
For example, if our function was , our "inner" function is leaving .
Differentiating each gives and .
Therefore the derivative is .