Problem of the Week

Updated at Jul 14, 2014 5:22 PM

How would you differentiate \({x}^{7}\sec{x}\)?

Below is the solution.



\[\frac{d}{dx} {x}^{7}\sec{x}\]

1
Use Product Rule to find the derivative of \({x}^{7}\sec{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} {x}^{7})\sec{x}+{x}^{7}(\frac{d}{dx} \sec{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[7{x}^{6}\sec{x}+{x}^{7}(\frac{d}{dx} \sec{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\sec{x}\) is \(\sec{x}\tan{x}\).
\[7{x}^{6}\sec{x}+{x}^{7}\sec{x}\tan{x}\]

Done
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