Problem of the Week

Updated at Dec 7, 2015 3:58 PM

This week we have another calculus problem:

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

Let's start!



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

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

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

3
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[\sec{x}\tan{x}\ln{x}+\frac{\sec{x}}{x}\]

Done
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