Bonjour,
[tex]f(x)= \frac{(x^2+x)}{2} \\ \\ f'(x)= \frac{2x+1}{2} \\ \\ f'(x) = x+ \frac{1}{2}[/tex]
Df : IR
[tex]g(x)= \frac{3}{(x^2+2)} =3* \frac{1}{(x^2+2)} \\ \\ g'(x)= 3*\frac{0(x^2+2)-1*2x}{(x^2+2)^2} \\ \\ g(x')=3* \frac{-2x}{(x^2+2)^2} \\ \\ g'(x) = -\frac{6x}{(x^2+2)^2} [/tex]
Dg : IR
[tex]h(x)= \sqrt{x} (x+1) \\ \\ h'(x)= \frac{1}{2 \sqrt{x} } (x+1)+ \sqrt{x} \\ \\ h'(x)= \frac{x}{2 \sqrt{x} } + \frac{1}{2 \sqrt{x} } + \sqrt{x} \\ \\ h'(x)= \frac{1+x}{2 \sqrt{x} }+ \frac{ 2x}{2 \sqrt{x} } \\ \\ h'(x)= \frac{3x+1}{2 \sqrt{x} } [/tex]
Dh : IR+*
[tex]i(x)= \frac{x+1}{ \sqrt{x}} \\ \\ i'(x)= \frac{1( \sqrt{x} )-(x+1)( \frac{1}{2 \sqrt{x} }) }{ (\sqrt{x})^2} \\ \\ i'(x)= \frac{ \sqrt{x} -( \frac{x}{2 \sqrt{x}}+ \frac{1}{2 \sqrt{x} } ) }{x} \\ \\ i'(x)= \frac{ \sqrt{x} - \frac{1+x}{2 \sqrt{x} } }{x} \\ \\ i'(x)= \frac{x-1}{2(x \sqrt{x}) } [/tex]
Di : IR+*
