Question

Find the derivative of the function.
g(u) = (5+u^2)^5(3-9u^2)^8

Could someone please explain the steps that would lead me to the answer? I'm completely stuck.

Answer 1

We can solve this by differentiation of a function of a function.

Given
g(u) = (5+u^2)^5(3-9u^2)^8
let
p(u)=(5+u²), and
q(u)=(3-9u²)

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^2-1)^7*(39*u^2+115)
or some equivalent expression.

Answer 2

Go to : calc101 com

Click option derivatives

In rectacangle:Take the derivative of
type:

((5+u^2)^5)((3-9u^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 step-by-step

By the way on this site you can practice any kind of derivation.