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Verified Answer :

\(y=(\sin(7x))^{\ln(x) } \\ \\ \ln{y}=\ln[(\sin(7x))^{\ln(x) }] \\ \\ \ln{y}=\ln(x)\ln[(\sin(7x))] \\ \\ (\ln{y})'=(\ln(x)\ln[(\sin(7x))])' \\ \\ \frac{1}{y} dy=[\frac{1}x}\ ln \sin(7x) +\frac{7 \cos (7x)}{sin(7x)}\ln{x}] dx \\ \\ \frac{dy}{dx} =y[\frac{1}x}\ ln \sin(7x) +\frac{7 \cos (7x)}{sin(7x)}\ln{x}] \\ \\ \frac{dy}{dx} =(\sin(7x))^{\ln(x) }[\frac{1}x}\ ln \sin(7x) +\frac{7 \cos (7x)}{sin(7x)}\ln{x}]\)

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