Problem of the Week

Updated at Mar 12, 2018 8:50 AM

This week's problem comes from the calculus category.

How can we solve for the derivative of \(\tan{x}\sec{x}\)?

Let's begin!



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

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

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

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

Done
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