Problem of the Week

Updated at Jul 3, 2017 11:52 AM

How would you differentiate \(2x+\cot{x}\)?

Below is the solution.



\[\frac{d}{dx} 2x+\cot{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} 2x)+(\frac{d}{dx} \cot{x})\]

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

3
Use Trigonometric Differentiation: the derivative of \(\cot{x}\) is \(-\csc^{2}x\).
\[2-\csc^{2}x\]

Done
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