Implicit Differentiation

In the previous post we have discussed about inverse trig functions and In today's session we are going to discuss about Implicit Differentiation. Hello friends today we will be discussing a new topic Implicit Differentiation Calculator, firstly we will talk about the normal differentiation then we will move to  implicit differentiation, if we talk about normal differentiation then in normal differentiation we differentiate with respect to one variable  as if have to differentiate  y = 7x+y  with respect to x then  the differentiation will be dy /dx = 7 ,  as we are differentiating with respect to x so all the variable which are not having x with them the differentiation  of them will be 0.  But in implicit differentiation we will differentiate with respect to both the function x and y.  As in the above case the differentiation of y was zero but if we do implicit differentiation then the differentiation of y will not be zero it will be dy/dx.
Step 1: in this step we have to separate the terms, means the term containing x one side and term containing y one side.  (know more about Implicit and explicit functions , here)
Step 2: the term which don’t have x and y will be treated as constant and we have to differentiate the other terms..
Step 3: now find the value of dy/dx and that will be the solution for the given problem.
Now we will see one example in which we will do the implicit differentiation of a function.
Example: find the implicit differentiation of
Y = 3x + 4y2
Solution
Step 1: we have to separate the terms as,
Y – 4y2 =3x
Step 2 :  dy /dx – 8y* dy/dx = 3
Take dy/dx as common
Dy/dx (1 – 8y) =3
Step 3:
Dy/dx = 3/(1 -8y)
This is the required solution for the given problem.
In this way we can find the implicit differentiation of any function.
If you are appearing in Karnataka board then go through the topic What is Median , it is very important from exam point of view.