Problem of the Week

Updated at Feb 27, 2017 4:32 PM

How can we solve for the derivative of \(\tan{x}+\cos{x}\)?

Below is the solution.



\[\frac{d}{dx} \tan{x}+\cos{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} \tan{x})+(\frac{d}{dx} \cos{x})\]

2
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[\sec^{2}x+(\frac{d}{dx} \cos{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[\sec^{2}x-\sin{x}\]

Done
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