Problem of the Week

Updated at Dec 4, 2023 8:07 AM

How would you differentiate \(\csc{n}+\ln{n}\)?

Below is the solution.



\[\frac{d}{dn} \csc{n}+\ln{n}\]

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

2
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[-\csc{n}\cot{n}+(\frac{d}{dn} \ln{n})\]

3
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[-\csc{n}\cot{n}+\frac{1}{n}\]

Done
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