Math SOmeone please please help
posted by Anonymous .
Find the derivative of the function.
g(u) = (5+u^2)^5(39u^2)^8
Could someone please explain the steps that would lead me to the answer? I'm completely stuck.

We can solve this by differentiation of a function of a function.
Given
g(u) = (5+u^2)^5(39u^2)^8
let
p(u)=(5+u²), and
q(u)=(39u²)
Then
g(u)=p(u)^5 * q(u)^8
Using the chain rule, we get
d(p(u)^5)/du
=5p(u)^4*dp(u)/du
=5p(u)^4*2u ...(1)
Similarly,
d(q(u)^8)/du
=8q(u)^7*d(q(u))/du
=9q(u)^7*(18u) ... (2)
Now apply the product rule to the original function g(u):
d(g(u))/du
=(p(u)^5*d(q(u))/du + d(p(u))/du * q(u)^8
Substitute (1) and (2) and simplify to get:
13122*u*(u^2+5)^4*(3*u^21)^7*(39*u^2+115)
or some equivalent expression. 
Go to : calc101 com
Click option derivatives
In rectacangle:Take the derivative of
type:
((5+u^2)^5)((39u^2)^8)
In rectacangle:with respect to:
type u
In rectacangle:and again with respect to
type u
Then click option: DO IT
You will see solution stepbystep
By the way on this site you can practice any kind of derivation.