Problem of the Week

Updated at Aug 28, 2023 2:44 PM

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

How can we solve for the derivative of \({u}^{5}+\cos{u}\)?

Check out the solution below!



\[\frac{d}{du} {u}^{5}+\cos{u}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{du} {u}^{5})+(\frac{d}{du} \cos{u})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[5{u}^{4}+(\frac{d}{du} \cos{u})\]

3
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[5{u}^{4}-\sin{u}\]

Done
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