implicit differentiation
posted by Ann on .
find the dy/dx for:
y^2=(2x^3)y+5x

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(2y2x^3) = 6x^2*y +5
dy/dx = [6x^2*y+5)/(2y2x^3) 
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)