Question

d/dy[(y-7/y+2)²]
Resposta 18(y-7)/(y+2)³

Answer 1

$f(y)= \bigg(\dfrac{y-7}{y+2}\bigg)^2\\\\\\f'(y)=f'(u)\cdot{u'(y)}\\f(u)=u^2\\f'(u)=2u\\\\u(y)=\bigg( \dfrac{y-7}{y+2}\bigg)\\\\\\u'(y)= \dfrac{g'(y)\cdot{h(y)}-g(y)\cdot{h'(y)}}{h(y)^2}\\\\\\g(y)=y-7\ ......\ g'(y)=1\\h(y)=y+2\ ......\ h'(y)=1\\\\\\u'(y)= \dfrac{(y-7)-(y+2)}{(y+2)^2}\\\\\\u'(y)= \dfrac{9}{(y+2)^2}\\\\\\f'(y)=2\cdot\bigg( \dfrac{y-7}{y+2}\bigg)\cdot \dfrac{9}{(y+2)^2}\\\\\\f'(y)= \dfrac{18(y-7)}{(y+2)^3}$