| $$f\left( x\right)$$ |
$$D_{f}$$ |
$$f^{\prime }\left( x\right)$$ |
$$D_{f^{\prime }}$$ |
| $$k\ (constante)$$ |
$$\mathbb{R}$$ |
$$0$$ |
$$\mathbb{R}$$ |
| $$x$$ |
$$\mathbb{R}$$ |
$$1$$ |
$$\mathbb{R}$$ |
| $$ax+b$$ |
$$\mathbb{R}$$ |
$$a$$ |
$$\mathbb{R}$$ |
| $$x^{2}$$ |
$$\mathbb{R}$$ |
$$2x$$ |
$$\mathbb{R}$$ |
| $$\frac{1}{x}$$ |
$$\mathbb{R}^{\ast}$$ |
$$-\frac{1}{x^{2}} $$ |
$$\mathbb{R}^{\ast}$$ |
| $$\sqrt{x} $$ |
$$\mathbb{R}_{+}$$ |
$$\frac{1}{2\sqrt{x} } $$ |
$$\mathbb{R}^{\ast }_{+}$$ |
| $$x^{n}\ avec\ n\in \mathbb{N}\ et\ n>1$$ |
$$\mathbb{R}$$ |
$$nx^{x-1}$$ |
$$\mathbb{R}$$ |
| $$\sin \left( x\right)$$ |
$$\mathbb{R}$$ |
$$\cos \left( x\right)$$ |
$$\mathbb{R}$$ |
| $$\cos \left( x\right)$$ |
$$\mathbb{R}$$ |
$$-\sin \left( x\right)$$ |
$$\mathbb{R}$$ |
| $$-\sin \left( x\right)$$ |
$$\mathbb{R}$$ |
$$-\cos \left( x\right)$$ |
$$\mathbb{R}$$ |
| $$-\cos \left( x\right)$$ |
$$\mathbb{R}$$ |
$$\sin \left( x\right)$$ |
$$\mathbb{R}$$ |
| $$\tan \left( x\right)$$ |
$$\mathbb{R}\diagdown \left( \frac{π }{2} \ mod\ 2π \right) $$ |
$$\frac{1}{\cos^{2} \left( x\right) } =1+\tan^{2} \left( x\right) $$ |
$$\mathbb{R}\diagdown \left( \frac{π }{2} \ mod\ 2π \right) $$ |
| $$u\left( x\right) +v\left( x\right) $$ |
$$D_{u}\cap D_{v}$$ |
$$u^{\prime }\left( x\right) +v^{\prime }\left( x\right) $$ |
$$D_{u^{\prime }}\cap D_{v^{\prime }}$$ |
| $$u\left( x\right) -v\left( x\right) $$ |
$$D_{u}\cap D_{v}$$ |
$$u^{\prime }\left( x\right) -v^{\prime }\left( x\right) $$ |
$$D_{u^{\prime }}\cap D_{v^{\prime }}$$ |
| $$k\cdot u(x)\ avec\ k\in \mathbb{R}$$ |
$$D_{u}$$ |
$$k\cdot u^{\prime }(x)$$ |
$$D_{u^{\prime }}$$ |
| $$u(x)\cdot v(x)$$ |
$$D_{u}\cap D_{v}$$ |
$$u^{\prime }(x)\cdot v(x)+u(x)\cdot v^{\prime }(x)$$ |
$$D_{u^{\prime }}\cap D_{v^{\prime }}$$ |
| $$\frac{1}{u\left( x\right) } $$ |
$$D_{u}\diagdown \{ x|u(x)=0\} $$ |
$$-\frac{u^{\prime }\left( x\right) }{u^{2}\left( x\right) } $$ |
$$D_{u^{\prime }}\diagdown \{ x|u(x)=0\} $$ |
| $$\frac{u\left( x\right) }{v\left( x\right) } $$ |
$$D_{v}\cap D_{u}\diagdown \{ x|u(x)=0\} $$ |
$$\frac{u^{\prime }\left( x\right) v\left( x\right) -u\left( x\right) v^{\prime }\left( x\right) }{v^{2}\left( x\right) } $$ |
$$D_{v^{\prime }}\cap D_{u^{\prime }}\diagdown \{ x|u(x)=0\} $$ |
| $$v(u\left( x\right) )=\left( v\circ u\left( x\right) \right) $$ |
$$D_{u}\cap \left\{ x|v\left( x\right) \in D_{v}\right\} $$ |
$$v^{\prime }\left( u\left( x\right) \right) \cdot u^{\prime }\left( x\right) $$ |
$$D_{u^{\prime }}\cap \left\{ x|v\left( x\right) \in D_{v^{\prime }}\right\} $$ |
| $$\left[ u\left( x\right) \right]^{n} $$ |
$$\mathbb{R}$$ |
$$n\left[ u\left( x\right) \right]^{n-1} \cdot u^{\prime }\left( x\right) $$ |
$$\mathbb{R}$$ |
| $$\sqrt{u\left( x\right) } $$ |
|
$$\frac{1}{2\sqrt{u(x)} } \cdot u^{\prime }\left( x\right) $$ |
|
| $$\sin \left[ u\left( x\right) \right] $$ |
|
$$\cos \left[ u\left( x\right) \right] \cdot u^{\prime }(x)$$ |
|
| $$\cos \left[ u\left( x\right) \right] $$ |
|
$$-\sin \left[ u\left( x\right) \right] \cdot u^{\prime }(x)$$ |
|
| $$\tan \left[ u(x)\right] $$ |
|
$$\frac{1}{\cos^{2} \left[ u\left( x\right) \right] } \cdot u^{\prime }\left( x\right) =1+\tan^{2} \left[ u\left( x\right) \right] \cdot u^{\prime }\left( x\right) $$ |
|
$$t_{A}:y=f^{\prime }\left( a\right) \left( x-a\right) +f\left( a\right) $$