Sum Rule

Reference > Calculus: Differentiation

Description
\[\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\]
Examples
\[\frac{d}{dx} \cos{x}+\sin{x}\]
1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\)
\[(\frac{d}{dx} \cos{x})+(\frac{d}{dx} \sin{x})\]

2
The derivative of \(\cos{x}\) is \(-\sin{x}\)
\[-\sin{x}+(\frac{d}{dx} \sin{x})\]

3
The derivative of \(\sin{x}\) is \(\cos{x}\)
\[\cos{x}-\sin{x}\]

Done