Posted by **Ann** on Saturday, May 17, 2008 at 9:34am.

find the dy/dx for:

y^2=(2x^3)y+5x

- implicit differentiation -
**drwls**, Saturday, May 17, 2008 at 10:42am
With y considered a function of x, differentiate both sides of the equation with respect to x. Then solve for dy/dx.

2y dy/dx = (2x^3) dy/dx + y*(6x^2)+ 5

dy/dx(2y-2x^3) = 6x^2*y +5

dy/dx = [6x^2*y+5)/(2y-2x^3)

- implicit differentiation -
**Reiny**, Saturday, May 17, 2008 at 10:45am
2y(dy/dx) = 2x^3(dy/dx) + (6x^2)y + 5

2y(dy/dx) - 2x^3(dy/dx) = (6x^2)y + 5

dy/dx(2y - 2x^3) = 6x^2y + 5

dy/dx = ((6x^2)y + 5)/(2y - 2x^3)

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