Problem of the Week

Updated at Sep 5, 2022 12:09 PM

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

How can we find the derivative of csc⁡v+9v\csc{v}+9v?

Check out the solution below!



ddvcsc⁡v+9v\frac{d}{dv} \csc{v}+9v

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddvcsc⁡v)+(ddv9v)(\frac{d}{dv} \csc{v})+(\frac{d}{dv} 9v)

2
Use Trigonometric Differentiation: the derivative of csc⁡x\csc{x} is −csc⁡xcot⁡x-\csc{x}\cot{x}.
−csc⁡vcot⁡v+(ddv9v)-\csc{v}\cot{v}+(\frac{d}{dv} 9v)

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
−csc⁡vcot⁡v+9-\csc{v}\cot{v}+9

Done
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