Solution assignment 25 Product and Quotient rule

Differentiate:

$y=1-e^{-x}$

This function can be differentiated term by term, but the second function is not in the list of standard functions. However, we can write:

$y=1-\displaystyle\frac{1}{e^x}$

and thus:

$y'=0-[\displaystyle\frac{1}{e^x}]'=-[\displaystyle\frac{1}{e^x}]'$

Now we apply the quotient rule:

$y'=-[\displaystyle\frac{1}{e^x}]'=-\displaystyle\frac{e^x\cdot0-1\cdot{e^x}}{(e^x)^2}=\displaystyle\frac{1}{e^x}$

If you are familiar with the chain rule you can get the same result easier.