Problem of the Week

Updated at Oct 12, 2015 10:24 AM

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

How can we find the derivative of \({x}^{6}+\tan{x}\)?

Check out the solution below!



\[\frac{d}{dx} {x}^{6}+\tan{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} {x}^{6})+(\frac{d}{dx} \tan{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[6{x}^{5}+(\frac{d}{dx} \tan{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[6{x}^{5}+\sec^{2}x\]

Done
Cymath foriOSAndroid