Differentiation using product rule?

[steve snash]

Homework Statement

Differentiate the following function with respect to x,
p(x) = (( x+5 )^2)*(( x+3 )^7)

Homework Equations

well the product rule is,
p(x)=(f)*(g)
p'(x)= (f')*(g)+(g')*(f)
and general differentiation is,
p'(x)=n(f)^(n-1)*n(g)^(n-1)

The Attempt at a Solution

well i used the product rule and got
(2(x+5))*((x+3)^7)+(7(x+3)^6)*((x+5)^2)
but this is said to be wrong how do i simplify it more or what have i done wrong?

 

[Dick]

What you did is right. They probably just want you to pull out the common factors to simplify it more.

 

[steve snash]

so i could go,
(2*x+10)*(x+3)^7+(7x+21)*(x+5)^2
then
(3x+13)^7+(8x+26)^2

 

[Dick]

so i could go,
(2*x+10)*(x+3)^7+(7x+21)*(x+5)^2
then
(3x+13)^7+(8x+26)^2

Your algebra is looking pretty seriously awful there. Whoa. Just factor out (x+5)*(x+3)^6 and collect the rest. Try and use only real algebra this time, and not just random symbol rearrangment, ok?

 

[steve snash]

so it works out to be,
((x+3)^6)*((9x^2)+(86x)+205)
cheers for the help

 

[Dick]

so it works out to be,
((x+3)^6)*((9x^2)+(86x)+205)
cheers for the help

That's one version. You could also write it as (x+3)^6*(x+5)*(9x+1). Whatever works, like I said your initial differentiation was correct as well.