Question

Find dx/dy by implicit differentiation for 2x^3 + x sqrt y - y^3? I'm okay with everything except the x sqrt y

Answer 1

Do you mean d/dy (2x^3 + x sqrt y - y^3) or d/dx (2x^3 + x sqrt y - y^3) ?

Answer 2

d/dy (2x^3 + x sqrt y - y^3) = x/(2*sqrt y) - 3y^2
d/dx (2x^3 + x sqrt y - y^3) = 6x^2 + sqrt y

Answer 3

rewrite \( \sqrt{y} \) as \( y^{\frac{1}{2}}\) and use the power rule to take the derivative