if y = (e^x)^7 find dy/dx

To solve the the problem we need to recognize what type of differentiation technique we shall be employing

y = (ex)7

the x unction which we are diferentiating is a power of an exponential function therefore we must employ a substituion method to solve this

if u = ex

therefore y = (u)7

dy/du = 7(u)6

we can say du/dx = ex

therefore dy/dx = dy/du  * du/dx

dy/dx = 7(ex)6 * ex

dy/dx = 7(ex)6​ * ex

dy/dx = 7(ex)7​

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