| Fonction $f(x) $ | dérivée $f'(x)$ |
| $b\ =\ Constante$ | $0$ |
| $x$ | $1$ |
| $a.x\ \times\ b$ | $a$ |
| $a.x^{n}$ | $a.n.x^{n-1}$ |
| $\frac{1}{x}$ | $\frac{-1}{x^{2}}$ |
| $\sqrt{x}$ | $\frac{1}{2.\sqrt{x}}$ |
| $\cos(x)$ | $-\sin(x)$ |
| $\sin(x)$ | $\cos(x)$ |
- $f(x)=\pi$ $\Leftrightarrow\ f'(x)\ =\ ...............$ - $f(x)=x^3$ $\Leftrightarrow\ f'(x)\ =\ ...............$ - $f(x)=x^{\frac23}$ $\Leftrightarrow\ f'(x)\ =\ ...............$ - $f(x)=x^{2007}$ $\Leftrightarrow\ f'(x)\ =\ ...............$
- $f(x)=\pi$ $\Leftrightarrow\ f'(x)\ =\ 0 $ - $f(x)=x^3$ $\Leftrightarrow\ f'(x)\ =\ 3x^{2}$ - $f(x)=x^{\frac23}$ $\Leftrightarrow\ f'(x)\ =\ \frac{2}{3}x^{\frac{-1}{3}}$ - $f(x)=x^{2007}$ $\Leftrightarrow\ f'(x)\ =\ 2007x^{2006}$
- $f(x)=50$ $\Leftrightarrow\ f'(x)\ =\ ...............$ - $f(x)=5x^3$ $\Leftrightarrow\ f'(x)\ =\ ...............$ - $f(x)=8x\ +\ 5$ $\Leftrightarrow\ f'(x)\ =\ ...............$ - $f(x)= 2x^{2}\ +\ 5x\ - \ 5$ $\Leftrightarrow\ f'(x)\ =\ ...............$ - $f(x)= 2x^{4}\ +\ 2x^{3}\ - \ 5$ $\Leftrightarrow\ f'(x)\ =\ ...............$ - $f(x)= 2x^{8}\ +\ \ln(x)\ - \ 3.\sqrt{x}$ $\Leftrightarrow\ f'(x)\ =\ ...............$
- $f(x)=50$ $\Leftrightarrow\ f'(x)\ =\ 0$ - $f(x)=5x^3$ $\Leftrightarrow\ f'(x)\ =\ 5\times 3x^{2}\ =\ 15x^{2}$ - $f(x)=8x\ +\ 5$ $\Leftrightarrow\ f'(x)\ =\ 8$ - $f(x)= 2x^{2}\ +\ 5x\ - \ 5$ $\Leftrightarrow\ f'(x)\ =\ 2\times2x^{1}\ + 5 =\ 4x\ +\ 5$ - $f(x)= 2x^{4}\ +\ 2x^{3}\ - \ 5$ $\Leftrightarrow\ f'(x)\ =\ 2\times 4x^{3}\ +\ 2\times 3x^{2}\ =\ 8x^{3}\ +\ 6x^{2}$ - $f(x)= 2x^{8}\ +\ \ln(x)\ - \ 3.\sqrt{x}$ $\Leftrightarrow\ f'(x)\ =\ 2\times 8x^{7}\ +\ \frac{1}{x}\ -\ 3\frac{1}{2\sqrt{x}}\ =\ 16x^{7}\ +\ \frac{1}{x}\ -\ \frac{3}{2\sqrt{x}}$
........................................................... ........................................................... ........................................................... ...........................................................
........................................................... ........................................................... ........................................................... ...........................................................
| Fonction $f(x) $ | dérivée $f'(x)$ |
| $Constante$ | $0$ |
| $(u\ +\ v)'$ | $u' \ +\ v'$ |
| $(u\ \times \ v)'$ | $u'\ \times\ v \ +\ u\ \times\ v'$ |
| $\frac{1}{v}$ | $\frac{-v'}{v^{2}}$ |
| $\left(\frac{u}{v}\right)'$ | $\frac{u'\ \times\ v \ -\ u\ \times\ v'}{v^{2}}$ |
| a$x^{n}$ | a.n.$x^{n-1}$ \\ |
| $\frac{u(x)}{v(x)}$ | $\frac{u'(x).v(x) \ - v'(x).u(x)}{[v(x)]^{2}}$ |
| u[v(x)] | v'.u'[v(x)] |
| $e^{u}$ | $u'e^{u}$ |
| $\ln(u)$ | $\frac{u'}{u}$ |
| sin(ax+b) | a.cos(ax+b) |
| cos(ax+b) | -a.sin(ax+b) |