Implicit Differentiation Formula - Procedure and Solved Examples
Last Updated on Jul 31, 2023
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What is Implicit Differentiation?
Implicit differentiation is a method used to find the derivative of an implicit function. In this process, we differentiate an implicit equation with respect to the variable x, considering other variables as undefined functions of x.
Methods of Implicit Differentiation
There are two common ways to differentiate an implicit function:
- The first method involves solving the implicit equation for y, expressing it explicitly in terms of x, and then differentiating y. This method is particularly useful when y can be easily expressed in terms of x.
-
The second method involves considering y as a function of x and differentiating both sides of the implicit equation with respect to x. The derived equation is then solved to find the value of
.
Examples of Implicit Differentiation
Example 1: Find the derivative of the implicit function
Solution:
The given implicit function is,
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Frequently Asked Questions
What is implicit differentiation?
Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable x while treating the other variables as unspecified functions of x.
What are the methods to differentiate an implicit function?
1. Solve the implicit equation for y and express it explicitly in terms of x and differentiate. 2. Consider y as a function of x, differentiate both members of the implicit equation w.r.t x and solve the resulting equation to find the value of dy/dx.
How to calculate the implicit derivative of x²-5xy+3y²=7?
Differentiate the given function w.r.t x and rearrange the terms to find dy/dx. The derivative dy/dx for the given function is (2x-5y)/(5x-6y).
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