How do you find the derivative of Y=exexex+ex?

1 Answer
Jul 31, 2016

dYdx=4(ex+ex)2.

Explanation:

To find the derivative, we have to use the Quotient Rule, and, the Chain Rule, given below for ready reference :-

The Quotient Rule :- ddx(uv)=vdudxudvdxv2.

By the Chain Rule, ddxeax=eaxddx(ax)=aeax.

As a particular case of this, we have, ddxex=ex.

Hence,

dYdx

=(ex+ex)ddx(exex)(exex)ddx(ex+ex)(ex+ex)2

=(ex+ex)(ex(ex))(exex)(exex)(ex+ex)2

=(ex+ex)2(exex)2(ex+ex)2

=4(ex+ex)2.

In fact, if we use hyperbolic funs., then, since Y=tanhx, we can directly say that dYdx=sech2x=4(ex+ex)2.