Help Notes: Use logarithmic differentiation to find the derivative of the function: `y = (sin 9x)^(lnx)`

Tuesday, 16 October 2012

Use logarithmic differentiation to find the derivative of the function: $\displaystyle{y}={{\left({\sin{{9}}}{x}\right)}}^{{{\ln{{x}}}}}$

The
derivative of $\displaystyle{y}={{\left({\sin{{9}}}{x}\right)}}^{{{\ln{{x}}}}}$ has to be determined.

$\displaystyle{y}={{\left({\sin{{9}}}{x}\right)}}^{{{\ln{}}}}$
x)

take the natural logarithm of both the sides

$\displaystyle{\ln{{y}}}=$
ln((sin 9x)^(ln...

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