What is Implicit Differentiation?
Implicit Differentiation is the process of differentiation in which we differentiate the implicit function without converting it into an explicit function. For example, we need to find the slope of a circle with an origin at 0 and a radius r. Its equation is given as x2 + y2 = r2.
Now, to find the slope we need to find the dy/dx of the given function, so without implicit differentiation, we have to convert this function into an explicit function i.e., y = ∓√(r2 – x2) . The explicit function of this is comparatively hard to differentiate. Thus, we need to learn the implicit differentiation by which this can be very easily differentiated.
Read More: Calculus in Maths
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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