Problem of the Week

Updated at Jan 4, 2016 8:32 AM

How can we solve for the derivative of \(\tan{x}+{x}^{5}\)?

Below is the solution.



\[\frac{d}{dx} \tan{x}+{x}^{5}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} \tan{x})+(\frac{d}{dx} {x}^{5})\]

2
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[\sec^{2}x+(\frac{d}{dx} {x}^{5})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\sec^{2}x+5{x}^{4}\]

Done
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