Problem of the Week

Updated at Oct 7, 2019 12:39 PM

To get more practice in calculus, we brought you this problem of the week:

How can we find the derivative of ln⁡m+sec⁡m\ln{m}+\sec{m}?

Check out the solution below!



ddmln⁡m+sec⁡m\frac{d}{dm} \ln{m}+\sec{m}

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)).
(ddmln⁡m)+(ddmsec⁡m)(\frac{d}{dm} \ln{m})+(\frac{d}{dm} \sec{m})

2
The derivative of ln⁡x\ln{x} is 1x\frac{1}{x}.
1m+(ddmsec⁡m)\frac{1}{m}+(\frac{d}{dm} \sec{m})

3
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
1m+sec⁡mtan⁡m\frac{1}{m}+\sec{m}\tan{m}

Done
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