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!
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