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At $x=9$, the equation of the tangent line to the graph of $y=g(x)$ is $$2x+11y=-37$$ What is the equation of the tangent line to $y=g(x^2)$ at $x=3$ and the equation of the tangent line to $y=(g(x))^2$ at $x=9$?

Please help guys, I've been trying to figure this out for an hour and no success.. I really appreciate it! Thanks!

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If you've been working at it for an hour, then you must have some work to show. What have you tried so far? – EuYu Oct 14 '12 at 2:35
up vote 5 down vote accepted

Welcome to the Chain Rule!

The derivative of $y=g(x^2)$ is $y'=2x*g(x^2)$,

and the derivative of $y=(g(x))^2$ is $y'=2*g(x)*g'(x)$.

Hopefully you can solve from here.

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