Problem of the Week

Updated at Nov 18, 2013 1:12 PM

How can we find the derivative of \(\ln{x}\tan{x}\)?

Below is the solution.



\[\frac{d}{dx} \ln{x}\tan{x}\]

1
Use Product Rule to find the derivative of \(\ln{x}\tan{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} \ln{x})\tan{x}+\ln{x}(\frac{d}{dx} \tan{x})\]

2
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[\frac{\tan{x}}{x}+\ln{x}(\frac{d}{dx} \tan{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[\frac{\tan{x}}{x}+\ln{x}\sec^{2}x\]

Done
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