Bonjour Melissa252
[tex]f(x)=2x^2+\dfrac{x}{x^2+2}[/tex]
[tex]f'(x)=(2x^2)'+(\dfrac{x}{x^2+2})'[/tex]
[tex]f'(x)=4x+\dfrac{x'\times(x^2+2)-x\times(x^2+2)'}{(x^2+2)^2}[/tex]
[tex]f'(x)=4x+\dfrac{1\times(x^2+2)-x\times(2x+0)}{(x^2+2)^2}[/tex]
[tex]f'(x)=4x+\dfrac{(x^2+2)-x\times(2x)}{(x^2+2)^2}[/tex]
[tex]f'(x)=4x+\dfrac{x^2+2-2x^2}{(x^2+2)^2}[/tex]
[tex]f'(x)=4x+\dfrac{2-x^2}{(x^2+2)^2}[/tex]
[tex]f'(x)=\dfrac{4x(x^2+2)^2+2-x^2}{(x^2+2)^2}[/tex]
[tex]f'(x)=\dfrac{4x(x^4+4x^2+4)+2-x^2}{(x^2+2)^2}[/tex]
[tex]f'(x)=\dfrac{4x^5+16x^3+16x+2-x^2}{(x^2+2)^2}\\\\[/tex]
[tex]\boxed{f'(x)=\dfrac{4x^5+16x^3-x^2+16x+2}{(x^2+2)^2}}[/tex]
