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

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Answer 1 · 2015-03-27T02:26:09

For $f (x) = e^{2 x^{2}}$ $f(x)=e^(2x^2)$ , 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

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

What is the derivative of e^(2x^2)e2x2e^(2x^2)?