Problem of the Week

Updated at Mar 2, 2015 9:46 AM

For this week we've brought you this calculus problem.

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

Here are the steps:



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

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

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

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

4
Use Trigonometric Differentiation: the derivative of \(\cot{x}\) is \(-\csc^{2}x\).
\[8(\cot{x}-x\csc^{2}x)\]

Done
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