Question

Qual a derivada de F(x)= x²/1+x?

Answer 1

$(\dfrac{u}{v})'=\dfrac{u'v-uv'}{v^2}\\\\\\f(x)=\dfrac{x^2}{1+x}\\\\f'(x)=\dfrac{(x^2)'(1+x)-(x^2)(1+x)'}{(1+x)^2}=\\\\\dfrac{(2x)(1+x)-(x^2)(1)}{(1+x)^2}=\\\\\dfrac{2x+2x^2-x^2}{(1+x)^2}=\\\\\dfrac{x^2+2x}{(1+x)^2}$