Derivative Questions?

How do I solve these problems?????--to find the derivative
1. y=(x+1)^2(x^2+2x)

2. y=x/x+1

Hi there montenegro3, welcome to MHF!

Quote:

Originally Posted by montenegro3

How do I solve these problems?????--to find the derivative
1. y=(x+1)^2(x^2+2x)

To differentiate this function you must employ the product rule.

It states that if

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

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

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

Quote:

Originally Posted by montenegro3

2. y=x/x+1

Use the quotient rule here, it states if

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

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

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

Instead of the quotient rule, you should rewrite that ratio as...

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

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