Problem of the Week

Updated at Jul 27, 2015 2:12 PM

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

Below is the solution.



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

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

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

3
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[1-\csc{x}\cot{x}\]

Done
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