Explain Different Types Of Differentiation

  In the 12th class, there is a total of 8 types of  Differentiation, I have prepared the best differentiation method for Class 12th, Each method is very easy & important,  plz take a complete look at these PDFs. because this is very helpful for you,  This is the best Notes not for only 12th class but even Higher-Studies.

8 Types of Differentiation.....

1. Simple Derivative Function......

This type of question is important for pre-board exams and sometimes for the Board exam

There are some steps of doing these differentials questions, I'll explain them to you one by one,

Step 1 ..👉👉

As you can see, if the function is easier to convert into power this function is an absolutely simple function,

then >>>

Step 2..👉👉

you have to differentiate both sides, and then

  your answer will come,

PDF FOR Simple Derivative Function

2. Inverse Derivative Function......

This type of question's is very important for both pre-Board and Board exams,,,,,,,,

 

for inverse differentiation, we have again a few steps. But before we move any further I would like to tell you there are few formulas that you should be aware of that because they are very important to solve these invrese types Questions,,

Step 1....👉👉

When we see  these inverse functions, we can clearly say that they have -1 power so they are inverse functions,,

Step 2..👉👉

we have to find out which function is that SIN/COS/TAN/COT/SEC/COSEC.

  Then we use them |

Step 3... 👉👉

Then differentiate them and your answer is here,😀😊

BUT SOME TIME YOU NEED TO ASSUME THE VALUE OF "X"

How to assume that value,

when you see your question is looks like a  trigonometry formula then assume the value of   "X"  according to your Question,

PDF FOR INVERSE FUNCTION'S

3. Logarithmic Derivative Function......

This type of questions is very important for both pre-Board and Board exams,,,,,,,,

Before moving any further we have some log formulas :

1. log m^n =  m.log n

2. log(m.n) = log m + log n

3. log(m/n) = log m - log n

The identity of the log functions is where the function is the power of function, you will be understood that when you see the questions>>>>>>

Step 1....👉👉

When you see the function like Y = (X)^X or Y = X^sin x, then you have to take log  to both sides and then, you have to function like     logY = log(X)^X,

THEN differentiate it 

Step 2....👉👉

after differentiating this function looks like 1/y*dy/dx =d/dx(function),

then solve them  with respective formulas of logs,

 NOTE:: your answer must be in the log form,

IF your questions be like  y = function1 - function2

Then solve it in part's,

PDF FOR LOG FUNCTIONS

4. Implicit Derivative Function......

Note= when you see  "X" and "Y" both in one differentiation equation so that means this is Implicit Derivative types of Qns. 

AND always give the answer in the form of  dy/dx

Now move ahead >>>>.

Step 1....👉👉 ( Differentiation)

Our first step is to differentiate the equation and then ..

Step 2....👉👉

When you differentiate the equation then do some calculations and then adjust the problem and then give the answer in  dy/dx form.

Pdf for Implicit functions

5. Infinite Series Derivative Function......

Note = In this differentiation Functions goes infinite power(function as a power)

Step 1....👉👉 

When you see  the function is the power  of a function then simply put the second power in the additional power of that function and add those two power,

    

Step 2....👉👉 ( log >> Differentiation)

Take log to both sides>> and then  Differentiate the problem, Then arrange it in a manner,

Note = Always remember that your problem In the  last  it will become 1/y*dy/dx

 

pdf for Infinite Functions

6. Parametric  Derivative Function......

IDENTITY NOTE = "There is always a third component with respect to which we  have to differentiate"

In this type of Questions, there is always both "X" and "Y",

Step 1....👉👉  

First Differentiate both equations partially, Always make  your first equation in form of "X"  {Eq(1)>>dx/dt} and second in form of "Y" {Eq(2)>>dy/dt} 

Step 2....👉👉 

Now you have two equations Eq(1) & Eq(2).

then divide ➗  Eq(2)/Eq(1), Now you have dy/dx.

PDF for Parametric Function's 

 7. Successive Derivative Function......(Higher - Order Diff.)

Identity = There is always you need to double or triple Differentiation 

These types of questions are very important for both In 12th or after 12th,

IN this type of Question they simply ask you to differentiate it in a Higher -Order (Double/Triple)

dy/dx           = y'

d^2y/dx^2   = y''

d^3y/dx^3   = y'''

Step 1....👉👉

See how much order you have to differentiate.

Then simply differentiate it.

Step 2....👉👉(If more than one order)

Differentiate it again-n-again with respect to Components(x,y, etc...),

PDF for Successive Function's 

8. Relative Derivative Function....

Identity >> They always said that  Differentiate it concerning this(Component),

Step 1....👉👉

First, separate those functions and,

and assume(anything) it,

as u see I have assumed it "U" AND "V" NOTE = assume the function first which we have found out the differentiation. 

Step 2....👉👉 

Now it will be the same as Parametric Functions. Then solve it and find your answer,

Pdf for Relative Functions

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