Find the derivative of e^2x.

e^2x is a natural exponential function where 'e' is an Euler number whose value is 2.718281828459... 

Answer: The derivative e^2x is 2 (e^2x).

To find the solution we will put f (x) = 2x. Here is the complete solution.

Explanation:

⇒ y = e^2x

We will use chain rule,

dy / dx = du / dx × dy / du

On differentiating the above equation with respect to 'u'.

⇒ Let u = 2 x

⇒ d / dx (u) = 2 du / dx

⇒ y = e^u

⇒ d / du (e^u) = e^u dy / du

Substitute the value in the chain rule

⇒ dy / dx = dy / du × du / dx

⇒ dy / dx = 2 (e^2x) 

Thus, the derivative e^2x is 2 ( e^2x ).