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August 30, 2014

Posted by **Anonymous** on Monday, February 21, 2011 at 11:15pm.

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.

- Math differentiation+substitution -
**MathMate**, Monday, February 21, 2011 at 11:31pmWe 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.

- Math SOmeone please please help -
**Bosnian**, Monday, February 21, 2011 at 11:47pmGo 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.

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