The discussion focuses on differentiating the implicit function defined by the equation 2x3 - 8xy + y2 = 1. The solution involves applying implicit differentiation, resulting in the equation 6x2 - 8y - 8x(dy/dx) + 2y(dy/dx) = 0. The final expression for dy/dx is derived as (8y - 6x2) / (2y - 8x), simplifying to (4y - 3x2) / (y - 4x). The discussion highlights the importance of factorization in reaching the explicit form of dy/dx.
PREREQUISITESStudents studying calculus, particularly those focusing on implicit differentiation, as well as educators seeking to enhance their teaching methods in calculus concepts.
1irishman said:Homework Statement
2x^3 - 8xy + y^2 = 1
Homework Equations
The Attempt at a Solution
d2x^3/dx - d8xy/dx + dy^2/dx = d1/dx
6x^2 -8(y) + dy/dx(-8x) + 2y(dy/dx) = 0
6x^2 - 8y -8x(dy/dx) + 2y(dy/dx) = 0 I am stuck and can't seem to go further. Someone help?
[/Qdy/dx = 8y-6x^2/2y-8x=4y-3x^2/y-4x
okay got it thank you. i skipped a couple of steps
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