Question

How do you find the derivative of `y=e^(2x)`?

Answer 1

By Chain Rule,
`y'=2e^{2x}`

Recall:
`(e^x)'=e^x`
Chain Rule: `[f(g(x))]'=f'(g(x))cdot g'(x)`

In the posted problem,
`f(x)=e^x` and `g(x)=2x`
By taking the derivative,
`f'(x)=e^x` and `g'(x)=2`

By Chain Rule,
`y'=e^{2x}cdot2=2e^{2x}`