Problem of the Week

Updated at Oct 10, 2016 9:09 AM

To get more practice in calculus, we brought you this problem of the week:

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

Check out the solution below!



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

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

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

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

Done
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