Prerequisite for Implicit Differentiation
There are some prerequisite concepts that we need to know before learning Implicit Differentiation, these prerequisites are as follows:
Chain Rule
The chain rule is a formula to compute the derivative of a composite function. That is, if f and g are differentiable functions, then the chain rule expresses the derivative of their composite f ∘ g as f(g(x))’ = f'(g(x)) × g'(x)
Implicit Function
When a function is not defined explicitly in terms of a single independent variable. Implicit Function is represented as f(x, y) = k, where k is a real number, then the function is called the implicit function. For example, y + x2 = 5, x2 + y2 = r2, etc.
Explicit function
When a function is defined in terms of a single independent variable explicitly such as y = f(x), then the function is called the explicit function. For example, y = x2, y = 3x+7, y = sin x, etc.
f(x, y) = 0 e.g. y + x2 = 5
Note: Here we took only 2 variables x and y to define the implicit function. But you can have any number of variables.
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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