find dy/dx by implicit differentiation if y^3+10xy+4x^3-12x=0

Question

stumped, need some help

Answer 1

y³+10xy+4x³-12x = 0 

Take the derivative of both sides with respect to x, considering y as an implicit function of x.   Use the power rule, chain rule and product rule.

3y²·dy/dx+(10y+10x·dy/dx)+12x²-12 = 0

(3y²+10x)dy/dx+2(5y+6x²-6) = 0

The answer is: dy/dx = -2(5y+6x²-6)/(3y²+10x),  (3y²+10x ≠ 0)

Answer 2

Given y^3+10xy+4x^3-12x=0
y'(x)=-[2(6x^2+5y-6)]/[10x+3y2]

Online Calculus Tutor - http://math.tutorvista.com/calculus.html

Answer 3

Let f(x,y)=y³+10xy+4x³-12x ··· Eq.1

Since f(x,y)=0, the total derivative, with respect to x, of both sides of f(x,y)=0 can be written as follows: 

∂f/∂x+(∂f/∂y)(dy/dx)=0   therefore, dy/dx=-(∂f/∂x)/(∂f/∂y) ··· Eq.2

From Eq.1, ∂f/∂x=10y+12x²-12, and ∂f/∂y=3y²+10x   Thus, from Eq.2, we have:

dy/dx=-(10y+12x²-12)/(3y²+10x)=-2(5y+6x²-6)/(3y²+10x)

The answer is: dy/dx=-2(5y+6x²-6)/(3y²+10x)