Question

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

Answer 1

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)`.