P r o d u c t R u l e {\displaystyle \color {Purple}Product\,Rule} d d x [ f ⋅ g ] = d d x [ f ] ⋅ g + d d x [ g ] ⋅ f {\displaystyle {\frac {d}{dx}}[f\cdot {g}]={\frac {d}{dx}}[f]\cdot {g}+{\frac {d}{dx}}[g]\cdot {f}} Q u o t i e n t R u l e {\displaystyle \color {Blue}Quotient\,Rule} d d x [ f g ] = d d x [ f ] ⋅ g − d d x [ g ] ⋅ f g 2 {\displaystyle {\frac {d}{dx}}[{\frac {f}{g}}]={\frac {{\frac {d}{dx}}[f]\cdot {g}-{\frac {d}{dx}}[g]\cdot {f}}{g^{2}}}}
![{\displaystyle {\frac {d}{dx}}[f\cdot {g}]={\frac {d}{dx}}[f]\cdot {g}+{\frac {d}{dx}}[g]\cdot {f}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/57ee97cfd2a83cef00e5454484f44a5c99a73190)
![{\displaystyle {\frac {d}{dx}}[{\frac {f}{g}}]={\frac {{\frac {d}{dx}}[f]\cdot {g}-{\frac {d}{dx}}[g]\cdot {f}}{g^{2}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/33117095dc4fc9bab8b77262a36eac752e1beaa5)