Question

What is the derivative of e^(2x)

I am confused because the derivative e^x is e^x.
But they say you need to use the chain rule.

Which is f'(g(x))*g'(x).
I have used that on exponents but in this I just get, 2x * e^(2x-1) *e
Which is not the answer =/

Answer 1

Using the chain rule: The derivative of e^u is (e^u)(u'). Notice that e^u is rewritten exactly as is and then multiplied by the derivative of the exponent.
Let u=2x. So u'=2
So the derivative of e^u is e^(2x)*2 This can also be written as 2e^(2x).