Thread: Chain rule

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.

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.

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

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

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

The second problem follows in the exact same way.

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