Problem of the Week

Updated at Aug 12, 2019 12:32 PM

How can we solve for the derivative of \(\csc{q}+{q}^{7}\)?

Below is the solution.



\[\frac{d}{dq} \csc{q}+{q}^{7}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dq} \csc{q})+(\frac{d}{dq} {q}^{7})\]

2
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[-\csc{q}\cot{q}+(\frac{d}{dq} {q}^{7})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[-\csc{q}\cot{q}+7{q}^{6}\]

Done
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