Problem of the Week

Updated at May 25, 2015 8:48 AM

This week we have another calculus problem:

How can we find the derivative of sin⁡x+4x\sin{x}+4x?

Let's start!



ddxsin⁡x+4x\frac{d}{dx} \sin{x}+4x

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)).
(ddxsin⁡x)+(ddx4x)(\frac{d}{dx} \sin{x})+(\frac{d}{dx} 4x)

2
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
cos⁡x+(ddx4x)\cos{x}+(\frac{d}{dx} 4x)

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
cos⁡x+4\cos{x}+4

Done
Cymath foriOSAndroid