Chain rule

**Stuck Man** · February 13th 2010, 07:37 AM

I have differentiated two expressions but the book has different answers. They are (x^9+8x)^3 and (x^3-1)^5.

Could someone give me the answers to check? I was using the chain rule and Leibniz notation.

**ANDS!** · February 13th 2010, 08:09 AM

What is the exact problem - are those two expressions part of different problems? It is not clear from your question. Just rewrite the problem you wish to have assistance with.

**Stuck Man** · February 13th 2010, 08:30 AM

They are two different questions. The first equation is y=(x^9+8x)^3.

**ANDS!** · February 13th 2010, 08:54 AM

Then by the chain rule (as in your other problem), F(G(x)) is equal to F'(G(x))G'(x):

$F'(G(x)) = 3(x^{9}+8x)$
$G'(x)=9x^{8}+8$
$F'(G(x))G'(x)=3(x^{9}+8x)(9x^{8}+8) \Rightarrow 3(9x^{17}+16x^{9}+64x)$

The second problem follows in the exact same way.

**Stuck Man** · February 13th 2010, 09:27 AM

You have missed ^2 from (x^9+8x). I'm new to this but I've found my mistakes. Thanks.

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