Question

Продифференцируйте функцию:

F(x)= Х2 / х+3

Answer 1

$\f(x)=frac{x^2}{x 3}$</var></p> <p> </p> <p><img src=[/tex]\left(frac{f}{g}right)'=frac{f'g-fg'}{g^2}" title="\f(x)=frac{x^2}{x+3}\" title="\left(frac{f}{g}right)'=frac{f'g-fg'}{g^2}" title="\f(x)=frac{x^2}{x+3}\" alt="\left(frac{f}{g}right)'=frac{f'g-fg'}{g^2}" title="\f(x)=frac{x^2}{x+3}\" />

 

$\f(x)=frac{x^2}{x+3}$

 

$<var>\left(frac{f}{g}right)'=frac{f'g-fg'}{g^2}$

 

[tex]\f'(x)=frac{2x(x+3)-x^2}{x^2+6x+9}\ f'(x)=frac{2x^2+6x-x^2}{x^2+6x+9}\ f'(x)=frac{x^2+6x}{x^2+6x+9}\ " title="\left(frac{f}{g}right)'=frac{f'g-fg'}{g^2}" />

 

[tex]\f'(x)=frac{2x(x+3)-x^2}{x^2+6x+9}\ f'(x)=frac{2x^2+6x-x^2}{x^2+6x+9}\ f'(x)=frac{x^2+6x}{x^2+6x+9}\ " alt="\left(frac{f}{g}right)'=frac{f'g-fg'}{g^2}" />

 

[tex]\f'(x)=frac{2x(x+3)-x^2}{x^2+6x+9}\ f'(x)=frac{2x^2+6x-x^2}{x^2+6x+9}\ f'(x)=frac{x^2+6x}{x^2+6x+9}\ " />