Problem of the Week

Updated at Jul 11, 2016 9:18 AM

This week we have another calculus problem:

How can we find the derivative of \(4x\csc{x}\)?

Let's start!



\[\frac{d}{dx} 4x\csc{x}\]

1
Use Constant Factor Rule: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\).
\[4(\frac{d}{dx} x\csc{x})\]

2
Use Product Rule to find the derivative of \(x\csc{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[4((\frac{d}{dx} x)\csc{x}+x(\frac{d}{dx} \csc{x}))\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[4(\csc{x}+x(\frac{d}{dx} \csc{x}))\]

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

Done
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