If x^3+2x^2y-4y=7, then when x=1, dy/dx=

dy/dx when x = 1 is (4y + 3) / 2.

Step-by-step explanation:

x^3 + 2x^2y - 4y=7

Using implicit differentiation:

3x^2 + 4xy + 2x^2. dy/dx - 4 dy/dx = 0

2x^2. dy/dx - 4dy/dx = - 3x^2 - 4xy

dy/dx = (-3x^2 - 4xy) / (2x^2 - 4)

When x = 1:

dy/dx = (-3 - 4y) / - 2

= - 1 (4y + 3) / - 2

(4y + 3) / 2 (answer).