How do you perform implicit differentiation?

Implicit differentiation is used when the function you need to differentiate is not in the form y = f(x). For example: y⁴ + 3x² - 10 + 2y² = 4xThe first step is to differentiate each term of the equation with respect to x, using the above example:(d/dx)(y⁴) + (d/dx)(3x²) - (d/dx)(10) + (d/dx)(2y²) = (d/dx)(4x)You can then differentiate terms only involving x as normal. To differentiate a function of y with respect to x the chain rule must be applied. Using the example, this gives:(d/dy)(y⁴)(dy/dx) + 6x + (d/dy)(2y²)(dy/dx) = 4You can now differentiate the terms containing y with respect to y as normal:4y³(dy/dx) + 6x + 4y(dy/dx) = 4Now factor out (dy/dx):(dy/dx)(4y³ + 4y) = 4 - 6xDivide through to get the final answer:(dy/dx) = (4 - 6x) / (4y³ + 4y)