Find dy/dx by implicit differentiation given that y satisfies the following equation:

7*x^3-8*x^2*y-2*x*y^2=8, i.e., .

:confused:

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- Oct 4th 2006, 11:41 AMiceycoolImplicit differentiation
Find dy/dx by implicit differentiation given that y satisfies the following equation:

7*x^3-8*x^2*y-2*x*y^2=8, i.e., .

:confused: - Oct 4th 2006, 11:58 AMCaptainBlack
Differentiating we get

d/dx[7*x^3-8*x^2*y-2*x*y^2]=0,

then:

d/dx[7*x^3] - d/dx[8*x^2*y] - d/dx[2*x*y^2]=0,

simplifying the derivative in the first term:

[21*x^2] - d/dx[8*x^2*y] - d/dx[2*x*y^2]=0

Now the second term:

[21*x^2] - [16*x*y+8*x^2 * dy/dx] - d/dx[2*x*y^2]=0

Now the third term:

[21*x^2] - [16*x*y+8*x^2 * dy/dx] - [2*y^2+4*x*y * dy/dx]=0

Now simplify to:

dy/dx = [21*x^2 - 16*x*y - 2*y^2]/[8*x^2 + 4*x*y]

RonL

(please check this carefully)

Checked by PerfectHacker and confiremd.