Problem of the Week

Updated at Aug 5, 2019 5:22 PM

How would you differentiate 11w+sin⁡w11w+\sin{w}?

Below is the solution.



ddw11w+sin⁡w\frac{d}{dw} 11w+\sin{w}

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)).
(ddw11w)+(ddwsin⁡w)(\frac{d}{dw} 11w)+(\frac{d}{dw} \sin{w})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
11+(ddwsin⁡w)11+(\frac{d}{dw} \sin{w})

3
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
11+cos⁡w11+\cos{w}

Done
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