Problem of the Week

Updated at Aug 1, 2016 3:10 PM

This week's problem comes from the calculus category.

How would you differentiate \({x}^{9}\sec{x}\)?

Let's begin!



\[\frac{d}{dx} {x}^{9}\sec{x}\]

1
Use Product Rule to find the derivative of \({x}^{9}\sec{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} {x}^{9})\sec{x}+{x}^{9}(\frac{d}{dx} \sec{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[9{x}^{8}\sec{x}+{x}^{9}(\frac{d}{dx} \sec{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\sec{x}\) is \(\sec{x}\tan{x}\).
\[9{x}^{8}\sec{x}+{x}^{9}\sec{x}\tan{x}\]

Done
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