implicit differentiation???

[drumergirl7276]

find dy/dx: Y²=(x-1)/( x+1) i dont know how to solve this.

 

[pappus]

find dy/dx: Y²=(x-1)/( x+1) i dont know how to solve this.

According to your headline use implicit differentiation:

\(\displaystyle \displaystyle{\underbrace{y^2}_{\text{use chain-rule}}=\underbrace{\frac{x-1}{x+1}}_{\text{use quotient rule}}}\)

You'll get:

\(\displaystyle \displaystyle{2y \cdot y'=\frac{(x+1)-(x-1)}{(x+1)^2}=\frac2{(x+1)^2}}\)

Solve for y':

\(\displaystyle \displaystyle{y'=\frac2{(x+1)^2} \cdot \frac12 \cdot \sqrt{\frac{x+1}{x-1}}}\)

Simplify!