To differentiate the function e^(5x), we use the chain rule, which is a fundamental rule in calculus for differentiating composed functions.
The function can be seen as a composition of two functions: the exponential function e^u, where u = 5x. According to the chain rule, the derivative of e^u with respect to x is given by:
f'(x) = e^u * (du/dx)
Now, we find du/dx. Since u = 5x, we have:
du/dx = 5
Substituting back into our derivative formula, we get:
f'(x) = e^(5x) * 5
Thus, the derivative of e^(5x) is 5e^(5x).