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

1 Answer
Mar 27, 2015

For #f(x)=e^(2x^2)#, the derivative is #f'(x)=4xe^(2x^2)#.

To get this answer, we use the fact that the exponential function is its own derivative, together with the chain rule:

For #f(x)=e^(g(x))#, the derivative is: #f'(x)=e^(g(x)) g'(x)#,

In differential operator notation: #d/(dx)(e^u)=e^u (du)/(dx)#

For #f(x)=e^(2x^2)#, the derivative is

#f'(x)=e^(2x^2)*(4x)=4xe^(2x^2)#.