How do I go about taking the derivative of [(-8x^2-8)^8(8x^2+3)^10], I'm having a hard time executing it correctly to get the right answer. Can someone explain how to go about doing this, thanks! How do I go about taking the derivative of [(-8x^2-8)^8(8x^2+3)^10], I'm having a hard time executing it correctly to get the right answer. Can someone explain how to go about doing this, thanks! @Mathematics

Question

How do I go about taking the derivative of [(-8x^2-8)^8(8x^2+3)^10], I'm having a hard time executing it correctly to get the right answer. Can someone explain how to go about doing this, thanks!  How do I go about taking the derivative of [(-8x^2-8)^8(8x^2+3)^10], I'm having a hard time executing it correctly to get the right answer. Can someone explain how to go about doing this, thanks!  @Mathematics

agreene · Answer

Product rule, then chain rule it to death (I know you will need at least 2 chain rules)

anonymous · Answer

hahahha will do, but how do I go about product rule with the polynomial being raised to its appropriate power?

eyust707 · Answer

fun =)

agreene · Answer

make the powers part of your product.

Product rule:
$$\frac{d}{dx}(u*v)=v\frac{du}{dx}+u\frac{dv}{dx}$$
Let:
u= (-8x^2-8)^8
v= (8x^2+3)^10
that gets you to:
$$(8x^2+3)^{10}*\frac{d}{dx}((-8x^2-8)^8)+(-8x^2-8)^8*\frac{d}{dx}((8x^2+3)^{10})$$
From there, you're gonna need to chain rule to get those two derivatives evaluated.

anonymous · Answer

thanks man, you are awesome!

agreene · Answer

lol just looked, and wolfram does it this way... I coulda saved some time and just linked you to it: click show steps http://www.wolframalpha.com/input/?i=d%2Fdx++%5B%28-8x%5E2-8%29%5E8%288x%5E2%2B3%29%5E10%5D

anonymous · Answer

damn, that is an impressive website. Once again, thanks man!