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How do I find the derivative of this?

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rubsnick

 
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PostPosted: Thu Mar 12, 2009 2:27 pm


(3x^2+1)^7

It's supposed to give me

42x(3x^2+1)

Whenver I do it it just gives me

42x+7 or 21x^2+7.

Could someone just help me out with this POC!
PostPosted: Thu Mar 12, 2009 8:42 pm


FIRST!!

*ahem*

You need to use the chain rule. Consider the 'composite function'

(F o G)(x) = (3x^2+1)^7

Where

F(x) = x^7
and
G(x) = 3x^2+1

The chain rule essentially states that

(F o G)'(x) = F'(G(x))G'(x)

In your case

F'(x) = 7x^6
G'(x) = 6x

So you'll end up with

(F o G)'(x) = 7(3x^2+1)^6 (6x) = 42x(3x^2 + 1)^6

Morberticus

 
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Mathematics
 
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