Problem of the Week

Updated at Jul 31, 2017 11:10 AM

This week's problem comes from the calculus category.

How would you differentiate \(8x\tan{x}\)?

Let's begin!



\[\frac{d}{dx} 8x\tan{x}\]

1
Use Constant Factor Rule: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\).
\[8(\frac{d}{dx} x\tan{x})\]

2
Use Product Rule to find the derivative of \(x\tan{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[8((\frac{d}{dx} x)\tan{x}+x(\frac{d}{dx} \tan{x}))\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[8(\tan{x}+x(\frac{d}{dx} \tan{x}))\]

4
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[8(\tan{x}+x\sec^{2}x)\]

Done
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