Implicit Differentiation Techniques

Take the derivative of both sides with respect to y.

Take the derivative of both sides with respect to x.

Integrate both sides with respect to x.

Solve for y in terms of x.

Power Rule

Quotient Rule

Chain Rule

Product Rule

x'

d/dx

dx/dy

y'

They are multiplied by y'.

They are divided by y'.

They are moved to the right side of the equation.

They are moved to the left side of the equation.

(2y - 2x) / (2y - 2x - 8)

(8y - 48) / (2x - 2y)

(24y - 2x + 400) / (32y - 24x - 300)

(12y - x + 200) / (16y - 12x - 150)

x^2 - 24xy + 16y^2 = 0

x - y^2 = 8(y - 6)

x^3 - 3xy + y^3 = 0

x^2 + y^2 = 1

0

1

x

y

By using the power rule

By using the quotient rule

By using the chain rule

By using the product rule

(y - x) / (y - x - 8)

(2y - 2x) / (2y - 2x - 8)

(8y - 48) / (2x - 2y)

(12y - x + 200) / (16y - 12x - 150)

To find the integral

To simplify the expression

To eliminate y

To eliminate x