[tex]y=\dfrac{x^2-8x}{x+2}\ \ ,\ \ x_0=0[/tex]

Производная дроби   [tex]\Big(\dfrac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}[/tex]  .

 [tex]y'=\dfrac{(2x-8)(x+2)-(x^2-8x)}{(x+2)^2}=\dfrac{2x^2+4x-8x-16-x^2+8x}{(x+2)^2}=\\\\\\=\dfrac{x^2+4x-16}{(x+2)^2}[/tex]  

[tex]y'(0)=\dfrac{-16}{4}=-4[/tex]