Sum Rule

Reference > Calculus: Differentiation

Description
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))
Examples
ddxcos⁡x+sin⁡x\frac{d}{dx} \cos{x}+\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)).
(ddxcos⁡x)+(ddxsin⁡x)(\frac{d}{dx} \cos{x})+(\frac{d}{dx} \sin{x})

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

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

Done

See Also

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