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27 March, 01:08

X

3

y-2x

2

+y

4

=8

Find / dfrac{dy}{dx}

dx

dy

.

+2
Answers (1)
  1. 27 March, 01:15
    0
    x^3y-2x^2+y^4=8

    take the derivative of each part, using the product rule on the first term

    x^3 dy + y*3x^2dx - 4xdx+4y^3 dy = 0

    gather the dy and dx terms together

    dy (x^3+4y^3) - dx (-3x^2y+4x) = 0

    dy terms on the left, dx terms on the right

    dy (x^3+4y^3) = dx (-3x^2y+4x)

    dy divided by dx

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

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