D [ f ( x ) ⋅ g ( x ) ] = f ′ ( x ) ⋅ g ( x ) + f ( x ) ⋅ g ′ ( x ) {\displaystyle \mathrm {D} [{f(x)\cdot g(x)}]=f'(x)\cdot g(x)+f(x)\cdot g'(x)}
D [ f ( x ) g ( x ) ] = f ′ ( x ) ⋅ g ( x ) − f ( x ) ⋅ g ′ ( x ) g ( x ) 2 {\displaystyle \mathrm {D} \!\left[{f(x) \over g(x)}\right]={f'(x)\cdot g(x)-f(x)\cdot g'(x) \over g(x)^{2}}}
D [ 1 f ( x ) ] = − f ′ ( x ) f ( x ) 2 {\displaystyle \mathrm {D} \!\left[{1 \over f(x)}\right]=-{f'(x) \over f(x)^{2}}\,\!}
D [ f − 1 ( y ) ] = 1 f ′ ( x ) {\displaystyle \mathrm {D} [f^{-1}(y)]={1 \over f'(x)}\,\!} , con y = f ( x ) {\displaystyle y={f(x)}}
D [ f ( g ( x ) ) ] = f ′ ( g ( x ) ) ⋅ g ′ ( x ) {\displaystyle \mathrm {D} \left[f\left(g(x)\right)\right]=f'\left(g(x)\right)\cdot g'(x)}
![{\displaystyle \mathrm {D} [{f(x)\cdot g(x)}]=f'(x)\cdot g(x)+f(x)\cdot g'(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bc918c90195d7cb3b3cec94f7271fc141ac020eb)
![{\displaystyle \mathrm {D} \!\left[{f(x) \over g(x)}\right]={f'(x)\cdot g(x)-f(x)\cdot g'(x) \over g(x)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a848c2328d398ba22ae09e72a1124fecd966d1d6)
![{\displaystyle \mathrm {D} \!\left[{1 \over f(x)}\right]=-{f'(x) \over f(x)^{2}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ca6ab9d7d8fc02d14652b23c6915c3886f552ec)
![{\displaystyle \mathrm {D} [f^{-1}(y)]={1 \over f'(x)}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b56dc7fe142113d21d781ca9f2aec2fad29dbaa)
, con 
![{\displaystyle \mathrm {D} \left[f\left(g(x)\right)\right]=f'\left(g(x)\right)\cdot g'(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c6612d72dfc0b1b0e1ab50ce666d502ddefa57dd)
