Second derivative

Question

Find the second derivative d^₂y/dx² of the function defined implicitly by the equation.
x^1/3 + y^1/3 = 94
d²y/dx² = ___________

Answer 1

x^1/3 + y^1/3 = 94

(1/3)x^1/3-1+(1/3)y^1/3-1(dy/dx)=0

(1/3)(-2/3)x^1/3-2+(1/3)(-2/3)y^1/3-2(dy/dx)²+(1/3)y^-2/3(d²y/dx²)=0 

(2/3)x^-5/3+(2/3)y^-5/3(dy/dx)² - y^-2/3(d²y/dx²)=0

y^-2/3d²y/dx²=(2/3)x^-5/3+(2/3)y^-5/3(dy/dx)²

d²y/dx²=(2/3)x^-5/3y^2/3+(2/(3y))(dy/dx)^2.