Difference between Implicit and Explicit Differentiation
Implicit Differentiation and Explicit Differentiation are the two methods of differentiation that are used in calculus. The differences between them are explained in the table below,
Implicit Differentiation | Explicit Differentiation |
---|---|
Used to find the derivative of a function that cannot be easily solved for y | Used to find the derivative of a function that can be easily solved for y |
Does not require the function to be expressed in terms of y | Requires the function to be expressed in terms of y |
Treats y as an implicit function of x | Treats y as an explicit function of x |
Involves taking the derivative of both sides of the equation with respect to x | Involves directly differentiating the function with respect to x |
Involves the chain rule and product rule to differentiate the function | Involves the power rule, product rule, quotient rule, and chain rule to differentiate the function |
Often used when solving equations that involve multiple variables or when finding higher-order derivatives | Often used when finding the slope of a tangent line or the instantaneous rate of change of a function |
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Implicit Differentiation
Implicit Differentiation is a useful tool in the arsenal of tools to tackle problems in calculus and beyond which helps us differentiate the function without converting it into the explicit function of the independent variable. Suppose we don’t know the method of implicit differentiation. In that case, we have to convert each implicit function into an explicit function, which is sometimes very hard and sometimes it is not even possible.
Implicit differentiation makes these problems very easy to solve. In this article, we will learn all the necessary basics we need to know about implicit differentiation formula, chain rule, implicit differentiation of inverse trigonometric functions, etc.
Table of Content
- What is Implicit Differentiation?
- Prerequisite for Implicit Differentiation
- Chain Rule in Implicit Differentiation
- Implicit Differentiation Formula
- How to do Implicit Differentiation
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