Problem of the Week

Updated at Feb 8, 2016 8:57 AM

How can we find the derivative of \(7x-\tan{x}\)?

Below is the solution.



\[\frac{d}{dx} 7x-\tan{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} 7x)-(\frac{d}{dx} \tan{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[7-(\frac{d}{dx} \tan{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[7-\sec^{2}x\]

Done
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