- [[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)