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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

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

Grade:

1 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

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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