Problem of the Week

Updated at Dec 14, 2015 8:00 AM

This week's problem comes from the calculus category.

How can we find the derivative of \(\sin{x}+{x}^{4}\)?

Let's begin!



\[\frac{d}{dx} \sin{x}+{x}^{4}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} \sin{x})+(\frac{d}{dx} {x}^{4})\]

2
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[\cos{x}+(\frac{d}{dx} {x}^{4})\]

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

Done
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