Question

Find dy/dx by implicit differentiation: X^3+(X^2)y+4y^2=6

Answer 1

So It's 3x^2 for the 1st part. Do I do the product rule for (x^2)y?

Answer 2

yes, but remember to chain the y

Answer 3

dy/dx = (dy/dy)(dy/dx)

Answer 4

yeah, thats where I get confused. Do i just add dy/dx to (x^2+2xy)? and turn it into:
x^2+2xy(dx/dy)?

Answer 5

*(dy/dx)

Answer 6

(d/dx) [x^3 + (x^2)y + 4y^2] = (d/dx)6

3x^2 + 2xy + 1 (dy/dx)(x^2) + 8y(dy/dx) = 0

Answer 7

m.. Where did the 1(dy/dx)x^2 come frome?

Answer 8

(d/dy)y = 1

Answer 9

oh! I think I see. Is this after u used the quotient rule? Cuz I got x^2+2yx (to the middle part

Answer 10

Can't u just leave it out?

Answer 11

[(d/dy)y] (dy/dx) = the derivative of y with respect to x
[(d/dy)y] (dy/dx) x^2

Answer 12

m.. I'm having trouble understanding. Plus it's getting late. I realy appreciate you taking the time to help me. But I'm going to ask my teacher for help. Thank you so much!

Answer 13

no problem