Implicit Differentiation Formula

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Differentiation

In implicit differentiation we differentiate each side of an equation with two variables usually x and y by treating one of the variables as a function of the other This calls for using the chain rule Let s differentiate x 2 y 2 1 for example Here we treat y as an implicit function of x To perform implicit differentiation on an equation that defines a function y implicitly in terms of a variable x, use the following steps: Take the derivative of both sides of the equation. Keep in mind that y is a function of x. Consequently, whereas. d d x ( sin x) = cos x, d d x ( sin y) = cos y d y d x.

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Implicit Differentiation FormulaIn this section we will discuss implicit differentiation. Not every function can be explicitly written in terms of the independent variable, e.g. y = f(x) and yet we will still need to know what f'(x) is. Implicit differentiation will allow. Implicit differentiation is a technique based on the Chain Rule that is used to find a derivative when the relationship between the variables is given implicitly rather than explicitly solved for one variable in terms of the other We begin by reviewing the Chain Rule Let f and g be functions of x