Problem of the Week

Updated at Jul 18, 2016 11:37 AM

How would you differentiate \(\cos{x}-{x}^{9}\)?

Below is the solution.



\[\frac{d}{dx} \cos{x}-{x}^{9}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} \cos{x})+(\frac{d}{dx} -{x}^{9})\]

2
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[-\sin{x}+(\frac{d}{dx} -{x}^{9})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[-\sin{x}-9{x}^{8}\]

Done
Cymath foriOSAndroid