AP03-02

retour

a. $f^{\prime }(x)=2x-{\displaystyle \frac{1}{2\sqrt{x}}}$;

b. $f^{\prime }(x)={\displaystyle \frac{3(2x+3)-2(3x-1)}{(2x+3{)}^2}}={\displaystyle \frac{11}{(2x+3{)}^2}}$.

c. $f^{\prime }(x)={\displaystyle \frac{3x^2(1+x)-(1+x^3)\times 1}{(1+x{)}^2}}={\displaystyle \frac{3x^2+3x^3-1-x^3}{(1+x{)}^2}}$
$={\displaystyle \frac{2x^3+3x^2-1}{(1+x{)}^2}}$;

d. $f^{\prime }(x)={\displaystyle \frac{-2x}{2\sqrt{1-x^2}}}=-{\displaystyle \frac{x}{\sqrt{1-x^2}}}$;

e. $f^{\prime }(x)=\sqrt{4-x}+x\times {\displaystyle \frac{-1}{2\sqrt{4-x}}}={\displaystyle \frac{8-2x-x}{2\sqrt{4-x}}}$
$={\displaystyle \frac{8-3x}{2\sqrt{4-x}}}$;

f. $f^{\prime }(x)=4(2x-2)(x^2-2x{)}^3=8x^3(x-1)(x-2{)}^3$;

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

h. $f^{\prime }(x)=-4\sin (4x-1)$.

retour

code : 171