Question

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

Answer 1

You can use the chain rule to find the first derivative of `e^(2x)` and differentiate iteratively

Explanation:

`(de^(2x))/dx = (de^(2x))/(d(2x)) * (d(2x))/dx = 2e^(2x)`

`(d^((2))e^(2x))/dx^2 =4e^(2x)`

`(d^((3))e^(2x))/dx^3 =8e^(2x)`

`(d^((4))e^(2x))/dx^4 =16e^(2x)`

In general it is easy to see that:

`(d^((n))e^(alpha x))/dx^n =alpha^n e^(alphax)`