- [[product rule]], [[chain rule]], [[derivative]]
# Idea
$
\frac{d}{d x}[g(x)+h(x)]=\frac{d g}{d x}+\frac{d h}{d x}
$
## Intuition
The output of the two functions are literally summed, and their derivatives are also summed.
![[s20220810_221954.png|600]]
## Examples
$
\frac{d}{d x}\left(\sin (x)+x^{2}\right)=\cos (x)+2 x
$
# References
- [3Blue1Brown - Visualizing the chain rule and product rule](https://www.3blue1brown.com/lessons/chain-rule-and-product-rule)