Problem of the Week

Updated at Jul 2, 2018 5:37 PM

How would you differentiate \(\ln{x}\sec{x}\)?

Below is the solution.



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

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

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

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

Done
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