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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
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