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# Implicit Differentiation Calculator

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Implicit differentiation is the method of differentiating an implicitly defined function by using chain rule. Differentiation of y takes place explicitly as the function of x.

Chain Rule:
Chain rule is a rule for evaluating the compositions of functions. Suppose if there are two functions y = f(u) and u = g(x) then,
chain rule is in the form of $\frac{dy}{dx}$$\frac{dy}{du} \times \frac{du}{dx}. This online implicit differentiation calculator will differenciate the given function using the chain rule. ## Steps Back to Top Step 1: Note the given equation in the problem. Step 2: Differentiate each term of the equation by using chain rule, \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}. ## Problems Back to Top Below are some of the problems based on implicit differentiation. ### Solved Examples Question 1: Find the derivative of implicitly defined function (x-y)^2=x+y-1 Solution: Step 1: Given : (x-y)^2=x+y-1 Step 2: Differenciating each term, \frac{d}{dx}$$[(x-y)^2]$=$\frac{d}{dx}$$[x+y-1] Using chain rule, 2(x-y)(1-\frac{dy}{dx})=1+\frac{dy}{dx} (2x-2y)(1-\frac{dy}{dx})=1+\frac{dy}{dx} (2x-2y)+(2y-2x)\frac{dy}{dx}=1+\frac{dy}{dx} (2y-2x-1)\frac{dy}{dx}=2y-2x+1 \frac{dy}{dx}=\frac{2y-2x+1}{2y-2x-1} Question 2: Find the derivative of implicitly defined function x^2+y^2=1. Solution: Step 1: Given : x^2+y^2=1 Step 2: Differenciating each term, \frac{d}{dx}(x^2+y^2)=\frac{d}{dx}(1) \frac{d}{dx}(x^2)+\frac{d}{dx}$$(y^2)$=0

Using chain rule,
2x+2y$\frac{dy}{dx}$=0

2y$\frac{dy}{dx}$=-2x

$\frac{dy}{dx}$=$\frac{-x}{y}$