Problem of the Week

Updated at Apr 4, 2016 3:25 PM

This week's problem comes from the calculus category.

How would you differentiate \({x}^{7}-\sin{x}\)?

Let's begin!



\[\frac{d}{dx} {x}^{7}-\sin{x}\]

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

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[7{x}^{6}-(\frac{d}{dx} \sin{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[7{x}^{6}-\cos{x}\]

Done
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