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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)

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Answered by Toby F. Maths tutor

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