Question

derivada regra da cadeia y = √ 3 x²- 4 x+6

Answer 1

 Consideremos $3x^2-4x+6=k$, então, $(6x-4)\,dx=dk$
 
 Segue que,

$y=\sqrt{3x^2-4x+6}\\y=\sqrt{k}\\y=k^{\frac{1}{2}}\\dy=(\frac{1}{2}\cdot\,k^{-\frac{1}{2}})\,dk$
 
 Substituindo $dk$ por $(6x-4)\,dx$, de acordo com a igualdade encontrada...

$dy=(\frac{1}{2}\cdot\,k^{-\frac{1}{2}})\,dk\\\\dy=\frac{1}{2}\cdot\,(3x^2-4x+6)^{-\frac{1}{2}}\cdot(6x-4)\,dx\\\\\frac{dy}{dx}=\frac{1}{2}\cdot(3x^2-4x+6)^{-\frac{1}{2}}\cdot2(3x-2)\\\\\boxed{\boxed{\frac{dy}{dx}=(3x^2-4x+6)^{-\frac{1}{2}}\cdot(3x-2)}}$