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April 16, 2014

April 16, 2014

Posted by **Adam** on Thursday, November 4, 2010 at 12:19am.

- Implicit diff. -
**MathMate**, Thursday, November 4, 2010 at 12:03pmtake log on both sides, and differentiate. Solve for y'.

y=9sin(x)^x

ln(y)=ln(9)+x*ln(sin(x))

differentiate:

(1/y)y' = ln(sin(x))+(x/sin(x))*cos(x)

y'=y(ln(sin(x))+(x/sin(x))*cos(x))

=9sin(x)^x * (ln(sin(x))+(x/sin(x))*cos(x))

Simplify the answer and check.

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