How do you implicitly differentiate -3=-x/(1-y)+3y?

Feb 17, 2018

$- \frac{1}{6 y}$.

Explanation:

Given that, $- 3 = - \frac{x}{1 - y} + 3 y$, we have,

$\frac{x}{1 - y} = 3 + 3 y = 3 \left(1 + y\right) , \mathmr{and} , x = 3 \left(1 + y\right) \left(1 - y\right)$.

$\therefore x = 3 \left(1 - {y}^{2}\right)$.

Diff.ing w.r.t. $y$, we have,

$\frac{\mathrm{dx}}{\mathrm{dy}} = 3 \left(0 - 2 y\right) = - 6 y$.

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{\frac{\mathrm{dx}}{\mathrm{dy}}} = - \frac{1}{6 y}$.