How do I solve these problems?????--to find the derivative

1. y=(x+1)^2(x^2+2x)

2. y=x/x+1

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- Dec 17th 2009, 06:16 PMmontenegro3Derivative Questions?
How do I solve these problems?????--to find the derivative

1. y=(x+1)^2(x^2+2x)

2. y=x/x+1 - Dec 17th 2009, 06:26 PMpickslides
Hi there montenegro3, welcome to MHF!

To differentiate this function you must employ the product rule.

It states that if

$\displaystyle y = u\times v \Rightarrow y' = vu'+uv'$

in your case make $\displaystyle u = (x+1)^2$ and $\displaystyle v = x^2+2x$

find $\displaystyle u'$ and $\displaystyle v'$ and apply the rule

Use the quotient rule here, it states if

For $\displaystyle y = \frac{u}{v} \Rightarrow y' = \frac{vu'-uv'}{v^2}$

in your case make $\displaystyle u = x $ and $\displaystyle v=x+1$

find $\displaystyle u'$ and $\displaystyle v'$ and apply the rule - Dec 18th 2009, 11:46 PMmatheagle
Instead of the quotient rule, you should rewrite that ratio as...

$\displaystyle {x\over x+1}={(x+1)-1\over x+1}= 1- {1\over x+1}= 1- (x+1)^{-1}$

Hence the derivative is $\displaystyle (x+1)^{-2}$