Problem of the Week

Updated at Jan 16, 2017 1:47 PM

How can we solve for the derivative of \(9x\cos{x}\)?

Below is the solution.



\[\frac{d}{dx} 9x\cos{x}\]

1
Use Constant Factor Rule: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\).
\[9(\frac{d}{dx} x\cos{x})\]

2
Use Product Rule to find the derivative of \(x\cos{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[9((\frac{d}{dx} x)\cos{x}+x(\frac{d}{dx} \cos{x}))\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[9(\cos{x}+x(\frac{d}{dx} \cos{x}))\]

4
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[9(\cos{x}-x\sin{x})\]

Done
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