Question

Please help with implicit differentiation. Find dy/dx for 4x^3+x^2y-xy^3 = -4

Answer 1

4x^3+x^2y-xy^3 = -4

we want derivatives with respect to x, so whenever we get a dx/dx, we get 1
So I will not write the dx/dx 's

12x^2 + (x^2)dy/dx + y(2x) - x(3y^2)dy/dx - y^3 = 0
dy/dx(x^2 - 3xy^2) = y^3 - 12x^2

dy/dx = (y^3 - 12x^2)/(x^2 - 3xy^2)

check my work, I tend to make errors when I don't do it on paper first
notice I needed to use the product rule for the 2nd and 3rd terms

Answer 2

Hi Reiny. According to my webwork. The answer it not correct. Any additional help?

Answer 3

sorry, I forgot the +2xy on the left side
should have been

dy/dx = (y^3 - 2xy - 12x^2)/(x^2 - 3xy^2)

I am disappointed that you could not find that simple error.

Answer 4

this problem has been a challenge for me.