Use implicit differentiation to find the second derivative y'' of the function given.

Question

x^2 + 5y^3 = 8

Answer 1

x^2 + 5y^3 = 8
2x + 15y^2 y' = 0
y' = -(2x)/(15y^2)

y" = - [(2)(15y^2)-(2x)(30yy')]/225y^4
= (60xyy'-30y^2)/(225y^4)
= (2xyy'-y^2)/(15y^4)
= (2xy'-y)/(15y^3)
= 2(2x(-(2x)/(15y^2))-y)/(15y^3)
= -2(4x^2+15y^3)/(225y^5)