Derivatives of Exp. Functions

Question

1. Find the general formula for the nth derivative of f(x) = e^(2x). Using the formula, evaluate nth derivative at x = 2 or f^n(1/2). -----> I got f^n(x) = 2^(n)e^(2x) for the general formula but im not sure if it's right and i don't know how to solve the second part of the question.

Answer 1

Hello Hilary

You are absolutely rright

If f(x) = e^x

f^'(x) = e^x

Here f^' (x) = 2e^2x

f^''(x) = 2*2 e^2x

and so on

fⁿ (x) = 2ⁿ e^2x

Now to find

nth derivative at x = 2 or f^n(1/2)

as X= 2 and n = √n

If, I understand it correctly

Plug in these values