Problem of the Week

Updated at Oct 30, 2017 9:48 AM

This week we have another calculus problem:

How can we find the derivative of x+sin⁡xx+\sin{x}?

Let's start!



ddxx+sin⁡x\frac{d}{dx} x+\sin{x}

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)).
(ddxx)+(ddxsin⁡x)(\frac{d}{dx} x)+(\frac{d}{dx} \sin{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
1+(ddxsin⁡x)1+(\frac{d}{dx} \sin{x})

3
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
1+cos⁡x1+\cos{x}

Done
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