Problem of the Week

Updated at May 2, 2016 2:17 PM

How can we solve for the derivative of \(\cot{x}-\ln{x}\)?

Below is the solution.



\[\frac{d}{dx} \cot{x}-\ln{x}\]

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

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

3
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[-\csc^{2}x-\frac{1}{x}\]

Done
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