What is the derivative of e^(2x)?

2 Answers
Jun 18, 2018

differentiate by parts

Explanation:

Derivative of e^x=e^x (always)
then
dy/dx=e^(2x)
now multiply the derivative of 2x withe^(2x)
dy/dx=2x
=(n)*x^(n-1)*2
the final answer
e^(2x)*2

Jun 22, 2018

2e^(2x)

Explanation:

Given: d/dx(e^(2x)).

Let y=e^(2x).

Use the chain rule, which states that,

dy/dx=dy/(du)*(du)/dx

Let u=2x,:.(du)/dx=2.

Then, y=e^u,:.dy/(du)=e^u.

Combining, we get:

dy/dx=e^u*2

=2e^u

Substituting back u=2x, we get the final answer:

color(blue)(barul(|=2e^(2x)|)