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 u5+cosu{u}^{5}+\cos{u}?

Check out the solution below!



dduu5+cosu\frac{d}{du} {u}^{5}+\cos{u}

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)).
(dduu5)+(dducosu)(\frac{d}{du} {u}^{5})+(\frac{d}{du} \cos{u})

2
Use Power Rule: ddxxn=nxn1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
5u4+(dducosu)5{u}^{4}+(\frac{d}{du} \cos{u})

3
Use Trigonometric Differentiation: the derivative of cosx\cos{x} is sinx-\sin{x}.
5u4sinu5{u}^{4}-\sin{u}

Done