How do you implicitly differentiate -y=xy+2sqrt(x-y^3) ?

Aug 18, 2017

dy/dx=-(x-y^3)^(1/2)/(x(x-y^3)^(1/2)+(1-3y^2)+(x-y^3)^(1/2)

Explanation:

$- \frac{\mathrm{dy}}{\mathrm{dx}}$$= x \frac{\mathrm{dy}}{\mathrm{dx}} + y +$...

$2 \sqrt{x + {y}^{3}} =$$2 {\left(x - {y}^{3}\right)}^{\frac{1}{2}}$ derivative of that equal to

${\left(x - {y}^{3}\right)}^{- \frac{1}{2}} \cdot \left(1 - 3 {y}^{2} \frac{\mathrm{dy}}{\mathrm{dx}}\right)$

with some math

get $\frac{\mathrm{dy}}{\mathrm{dx}}$ in one side and all in the other side

dy/dx=-(x-y^3)^(1/2)/(x(x-y^3)^(1/2)+(1-3y^2)+(x-y^3)^(1/2)

I need someone to check my answer or explain further, and I will be thankful.