Implicit Differentiation Formula with Problem Solution & Solved Example

Implicit differentiation is a popular term that uses the basic rules of differentiation to find the derivative of an equation that is not written in the standard form. The other popular form is explicit differentiation where x is given on one side and y is written on the other side. For a simple equation like x*y = 1, implicit differentiation is applicable here.

I am sure that you must have read about these types of derivatives earlier too during your Math studies. Here is given a simple example of derivative that almost everyone must be familiar with. Let us take a quick look below –

\[\ Y = 2x \]
\[\ Y’ = 2 \]

Mathematically, the standard form of derivation is y’ or dy / dx. Make sure that all standard rules of differentiation are still applicable for this simple equation too. In simple words, implicit differentiation is the simple implicit equation with respect to the desired variable x while treating other variables as specified functions of x. Here is a list of methods that can be used to find the differentiation of an implicit function.

In the First method, the implicit equation is solved for y and expressed implicitly in terms of x when differentiation is carried simply. This method is applicable when y can be expressed quickly in terms of x. For the second method, y is taken as the function of x and it is written as y = f (x). You could apply chain rule to find the derivative of implicit functions in mathematics.


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