How do you differentiate exponential function?

The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]

For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))

So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).

Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}

So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)