Solution assignment 25 Product and Quotient rule

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Assignment 25

Differentiate:

y=1-e^{-x}

Solution

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.

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