Problem of the Week

Updated at Jul 10, 2017 2:28 PM

This week we have another calculus problem:

How would you differentiate sec⁡x+ln⁡x\sec{x}+\ln{x}?

Let's start!



ddxsec⁡x+ln⁡x\frac{d}{dx} \sec{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)).
(ddxsec⁡x)+(ddxln⁡x)(\frac{d}{dx} \sec{x})+(\frac{d}{dx} \ln{x})

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

3
The derivative of ln⁡x\ln{x} is 1x\frac{1}{x}.
sec⁡xtan⁡x+1x\sec{x}\tan{x}+\frac{1}{x}

Done
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