Asked by John
Use implicit differentiation to find the second derivative y'' of the function given.
x^2 + 5y^3 = 8
x^2 + 5y^3 = 8
Answers
Answered by
Steve
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)
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)
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