Problem of the Week

Updated at Jun 2, 2025 1:00 PM

This week's problem comes from the calculus category.

How can we find the derivative of \(\cos{v}+{v}^{9}\)?

Let's begin!



\[\frac{d}{dv} \cos{v}+{v}^{9}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dv} \cos{v})+(\frac{d}{dv} {v}^{9})\]

2
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[-\sin{v}+(\frac{d}{dv} {v}^{9})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[9{v}^{8}-\sin{v}\]

Done
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