504

$D\left(\frac{3x}{x+1}\right)=$

$f\left(x\right)=3x{,}\ f'\left(x\right)=3\ ja\ g\left(x\right)=x+1{,}\ g'\left(x\right)=1$
$\frac{3\left(x+1\right)-3x\cdot1}{\left(x+1\right)^2}=\frac{3x+3-3x}{\left(x+1\right)^2}=\frac{3}{\left(x+1\right)^2}$

$D\left(\frac{x^2}{2x+1}\right)$
$f\left(x\right)=x^2{,}\ f'\left(x\right)=2x\ ja\ g\left(x\right)=2x+1{,}\ g'\left(x\right)=2$
$\frac{2x\left(2x+1\right)-2x^2}{\left(2x+1\right)^2}=\frac{4x^2+2x-2x^2}{\left(2x+1\right)^2}=\frac{2x^2+2x}{\left(2x+1\right)^2}$

$D\left(\frac{x}{1-x^2}\right)=$
$f\left(x\right)=x{,}\ f'\left(x\right)=1\ ja\ g\left(x\right)=1-x^2{,}\ g'\left(x\right)=-2x$
$\frac{x^2+1}{\left(1-x^2\right)^2}$