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December 21, 2014

December 21, 2014

Posted by **AHKSIJ** on Wednesday, December 7, 2011 at 12:08pm.

- calculus -
**Steve**, Wednesday, December 7, 2011 at 1:35pmf = g(e^2x)

f' = 2e^2x g'

f'' = 4e^2xg' + 2e^2xg''

example:

g(x) = x sinx

f(x) = g(e^2x) = e^2x sin(e^2x)

g' = sinx + xcosx

g'' = cosx + cosx - xsinx

= 2cosx - xsinx

f' = 2e^2x sin(e^2x) + e^2xcos(e^2x)*2e^2x

= 2e^2x(sin(e^2x) + e^2x cos(e^2x))

Letting g(e^2x) = g(u)

f' = 2e^2x g'(u)

I have expanded out

4e^2xg'(u) + 2e^2xg''(u)

and it checks out. Have lots of blank paper!

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