Problem of the Week

Updated at May 22, 2017 5:29 PM

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

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

Check out the solution below!



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

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

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

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

Done
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