# implicit differentiation

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find the dy/dx for:

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

• implicit differentiation -

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 -

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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