Calc
posted by Adam on .
Find the f'(3) of F(x)=9(sin(x))^x

take 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.