# Prove the identity by direct differentiation

• Oct 12th 2013, 05:44 AM
Prove the identity by direct differentiation
Hi, please have a look at the attached question and the attempt made to solve, but I can't
The question is Problem 1.2 (b)

The vectors in my working are underlined, but are bold in the question.

The thing is, that I don't know where the c springs from in the RHS.
Here is the question:

Attachment 29449

My attempt at solving:
Attachment 29450

Thanks for the help
• Oct 12th 2013, 07:56 AM
tom@ballooncalculus
Re: Prove the identity by direct differentiation
Just in case a picture helps...

http://www.ballooncalculus.org/draw/diffChain/nest6.png

... where (key in spoiler) ...

Spoiler:
http://www.ballooncalculus.org/asy/chain.png

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case t), and the straight dashed line (and in this more nested case also the squiggly line) similarly but with respect to the dashed (or squiggly) balloon expression (the inner function of the composite which is subject to the chain rule).

http://www.ballooncalculus.org/asy/prod.png

... is the product rule, where, again, straight continuous lines are differentiating downwards with respect to t.

Full size

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• Oct 12th 2013, 09:20 AM