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 = (e^x)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 = e^x

therefore y = (u)⁷

dy/du = 7(u)⁶

we can say du/dx = e^x

therefore dy/dx = dy/du  * du/dx

dy/dx = 7(e^x)⁶ * e^x

dy/dx = 7(e^x)^6​ * e^x

dy/dx = 7(e^x)^7​