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Solution assignment 30 Product and Quotient rule

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Assignment 30

Differentiate:

\displaystyle\frac{(x+1)^2}{e^{2x}}

Solution

We can write this function as follows:

y=e^{-2x}(x+1)^2

and apply the product rule:

y'=-2e^{-2x}(x+1)^2+e^{-2x}[(x+1)^2]'

We can write:

[(x+1)^2]'=[x^2+2x+1]'=2x+2

and thus:

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

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