Problem of the Week

Updated at Jun 15, 2015 5:33 PM

This week we have another calculus problem:

How can we find the derivative of \(\csc{x}-3x\)?

Let's start!



\[\frac{d}{dx} \csc{x}-3x\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} \csc{x})+(\frac{d}{dx} -3x)\]

2
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[-\csc{x}\cot{x}+(\frac{d}{dx} -3x)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[-\csc{x}\cot{x}-3\]

Done
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