AP03-02

retour

a. $f'(x) = 2x - \dfrac 1 {2\sqrt{x}}$;

b. $f'(x) = \dfrac{3(2x+3) - 2(3x-1)}{(2x+3)^2} =\dfrac{11}{(2x+3)^2}$.

c. $f'(x) = \dfrac{3x^2(1+x)-(1+x^3)\times 1}{(1+x)^2} =\dfrac{3x^2 + 3x^3 - 1 - x^3}{(1+x)^2}$
$=\dfrac{2x^3 + 3x^2 - 1}{(1+x)^2}$;

d. $f'(x) = \dfrac{-2x}{2\sqrt{1-x^2}} = -\dfrac{x}{\sqrt{1-x^2}}$;

e. $f'(x) = \sqrt{4-x}+ x\times\dfrac{-1}{2\sqrt{4-x}} =\dfrac{8-2x-x}{2\sqrt{4-x}}$
$= \dfrac{8-3x}{2\sqrt{4-x}}$;

f. $f'(x) = 4(2x-2)(x^2-2x)^3 = 8x^3(x-1)(x-2)^3$;

g. On peut écrire que $f(x) = (1-2x)^{-3}$, donc:
$f'(x) = -3(-2)(1-2x)^{-4} = \dfrac 6{(1-2x)^4}$;

h. $f'(x) = -4\sin(4x-1)$.

retour

code : 171