Problem of the Week

Updated at Jun 1, 2015 8:09 AM

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

How can we find the derivative of 7x−sin⁡x7x-\sin{x}?

Check out the solution below!



ddx7x−sin⁡x\frac{d}{dx} 7x-\sin{x}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddx7x)−(ddxsin⁡x)(\frac{d}{dx} 7x)-(\frac{d}{dx} \sin{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
7−(ddxsin⁡x)7-(\frac{d}{dx} \sin{x})

3
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
7−cos⁡x7-\cos{x}

Done
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