# Derivative Questions?

• Dec 17th 2009, 06:16 PM
montenegro3
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
• Dec 17th 2009, 06:26 PM
pickslides
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

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

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

Quote:

Originally Posted by montenegro3

2. y=x/x+1

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 PM
matheagle
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 $\displaystyle (x+1)^{-2}$