Question

Derivada:
a) √t-1/t+1
b) 4√1+2x+x³

Answer 1

Oi Seguem as derivadas 

a)

$y=\frac {\sqrt{t}-1 }{t+1} \\ \\ y'= \frac{(\sqrt{t}-1)'(t+1)-(\sqrt{t}-1)(t+1)'}{(t+1)^2} \\ \\ y'=\frac{ \frac{1}{2 \sqrt{t} } (t+1)-(\sqrt{t}-1)(1)}{(t+1)^2} \\ \\ y'= \frac{ \frac{t+1}{2 \sqrt{t} } -\sqrt{t}+1}{(t+1)^2} \\ \\ y'= \frac{ \frac{t+1-2 \sqrt{t}( \sqrt{t} )+2 \sqrt{t} }{2 \sqrt{t} }}{(t+1)^2} \\ \\ y'= \frac{t+1-2t+2 \sqrt{t} }{2 \sqrt{t} } . \frac{1}{(t+1)^2} \\ \\ y'= \frac{-t+ 2\sqrt{t} +1}{2 \sqrt{t}(t+1)^2 }$

b)

$y= \sqrt[4]{1} +2x+x^3 \\ \\ y'=0+2+3x^2 \\ \\ y'=3x^2+2$

Comenta Depois :)