Problem of the Week

Updated at Aug 11, 2014 2:48 PM

This week we have another calculus problem:

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

Let's start!



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

2
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
cos⁡x+(ddxln⁡x)\cos{x}+(\frac{d}{dx} \ln{x})

3
The derivative of ln⁡x\ln{x} is 1x\frac{1}{x}.
cos⁡x+1x\cos{x}+\frac{1}{x}

Done
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