How do you find the derivative of $y=e^(2x^2+2x)$ ?

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Answer 1 · 2018-04-14T22:27:21

$d/dxe^(2x^2+2x)=(4x+2)e^(2x^2+2x)$

This problem will require an application of the Chain Rule which, when applied to $e$ raised to the power of some function $u,$ tells us that

$d/dxe^u=e^u*(du)/dx$

Here, $u=2x^2+2x,$ so we have

$d/dxe^(2x^2+2x)=e^(2x^2+2x)*d/dx(2x^2+2x)$

$d/dx(2x^2+2x)=4x+2$ , so we end up with

$d/dxe^(2x^2+2x)=(4x+2)e^(2x^2+2x)$

How do you find the derivative of y=e^(2x^2+2x)y=e^(2x^2+2x)?