Question

derivada da função raiz (x)/(x+1)

obrigado

Answer 1

√x=x+1
√2x=1
√x=1:2
√0,5

Answer 2

Bom dia!

Solução!

Derivada do quociente!

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

$u=(x+1)~~~~u'=1\\\\\ v= \sqrt{x} ~~~~~v'=(x)^{ \frac{1}{2} }~~~~v'= \frac{1}{2} x^{- \frac{1}{2} }\\\\\ v'= \frac{1}{ 2\sqrt{x} }$

$f(x)= \dfrac{ \sqrt{x}.1-(x+1) \dfrac{1}{2 \sqrt{x} } }{(x+1)^{2} }\\\\\\ f(x)= \dfrac{ \sqrt{x}- \dfrac{(x+1)}{2 \sqrt{x} } }{(x+1)^{2} } \\\\\\ f(x)= \dfrac{2 \sqrt{x} . \sqrt{x} -(x+1)}{ \dfrac{2 \sqrt{x} }{(x+1)^{2} } }\\\\\\\\ f(x)= \dfrac{2x-x-1}{2 \sqrt{x} (x+1)^{2} }\\\\\\\\ f(x)= \dfrac{(x-1)}{2 \sqrt{x} (x+1)^{2} }$

Bom dia!

Bons estudos!