THE EQUESTION 4X^2Y-3Y=X^3 IMPLICITLY DEFINES y AS A FUNCTION OF X.

A)) USE IMPLICT DEFFERENTIATION TO DETERMINE dy/dx

B)) write y as an explicit function of x and compute dy/dx

C)) show that your results for part a and b are equivalent

using implicit differentiation 8xy+(4x^2)y'-3y'=3x^2, dy/dx=y'=(3x^2 -8xy)/(4x^2 -3)...(1)

y=(x^3)/(4x^2 -3), dy/dx=(1/(4x^2 -3)²)(3x²(4x^2 -3)-x³(8x))

from (1), dy/dx=(3x²(4x^2 -3)-8x^4)/(4x^2 -3)²

it is extremely easy to verify that the two methods give the same answer