Problem of the Week

Updated at Mar 31, 2014 4:53 PM

This week we have another calculus problem:

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

Let's start!



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

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

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

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

Done
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