# Math Help - chain rule question

1. ## chain rule question

hi guys
just a quick check to make sure im getting this right

$h(x)=f(g(x))$
where $f(x) = x^5$ and $g(x)=x^2+1$
so $h(x)=(x^2+1)^5$

$h'(x)=5(x^2+1)^4(2x)$ <---- heheh everyone noticed the type. Yes i meant h not f XD

now heres the part that confuses me. Is it correct to multiply the 5 before the brackets by the 2x to get
$10x(x^2+1)^4$?

Help appreciated

2. $h(x)=f(g(x))$
where $f(x) = x^5$ and $g(x)=x^2+1$
so $h(x)=(x^2+1)^5$

$f'(x)=5(x^2+1)^4(2x)$
I assume that you meant:

$h'(x)=5(x^2+1)^4(2x)$

Yes, you can multiply the $5$ and the $2x$ together. There is no rule against simplifying a derivative.