Question

Show that y2+ x-3 =0 is an implicit solution to dy/dx =-1/ (2y) on the interval (- [infinity] , 3)

Answer 1

Answer:

Implicit function

$\frac{d y}{d x} = \frac{-1}{2y}$

Step-by-step explanation:

Explanation:-

Given  y² + x - 3=0 ...(i)

Differentiating equation (i) with respective to 'x', we get

                   $2 y \frac{d y}{d x} +1 = 0$

           ⇒     $2 y \frac{d y}{d x} = -1$

           ⇒     $\frac{d y}{d x} = \frac{-1}{2y}$

                 $\frac{d y}{d x} = \frac{-1}{2 (3)}$

                 $\frac{d y}{d x} = \frac{-1}{6}$