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October 19th, 2012, 01:42 PM   #1
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Product rule into chain rule

I have this problem:

t^7(t^3+4)^6

Here are the steps I have so far, but I don't know where to simplify it even more.
Ok I'm going to do the product rule first

f'(x)g(x) + f(x)g'(x)
(7t^6)(t^3+4)^6 + (t7)(t^3+4)^6'
^^ so I have to use the chain rule on this last one. f'(g(x) times g'(x).
^^ I get 6(t^3+4)^5(3t^2)

Ok now I have my f' g f and g'
(7t^6)(t^3+4)^6 + (t7)6(t^3+4)^5(3t^2)
I have no idea where to go from here in terms of simplifying...
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October 19th, 2012, 01:49 PM   #2
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Re: Product rule into chain rule

You may clean up your result a bit to write:



Note that both terms have as factors, so we may write:

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October 19th, 2012, 01:56 PM   #3
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Re: Product rule into chain rule

Mark, how did you get the 18t^9(t^3+4)^5 from (t7)6(t^3+4)^5(3t^2)?!
You're a genius man lol.
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October 19th, 2012, 02:04 PM   #4
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Re: Product rule into chain rule

The 3 and the 6 have a product of 18 and the and the have a product of .
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October 19th, 2012, 02:21 PM   #5
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Re: Product rule into chain rule

gotcha thanks!
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