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Applied Mathematics - ll : Differentiation | Chapter 02 | Lecture 02 Notes For Polytechnic

Hey Everyone, How are you ... Today I will tell you what is differentiation ( Derivative ) & Geometric Interpretation of derivative Which is lecture 02 of Chapter 02 Differentiation Of Applied Mathematics 2 .

( Lecture -02 )

It's Very Important Lecture For All My students So Watch Video on youtube video & Download your Notes through below given link .

Lecture - 02 ( Topics ) :

1 ) What is differentiation Of A Function 

2 ) Geometric Interpretation Of Derivative .

3 ) Some Important Questions .

What Is Differentiation Of a Function 

Let be a Function = F ( x )

Then ,

  The derivative Of F ( x ) at c is defined by 

 F'( x ) = lim f ( c + h ) - f ( c ) / h 

               h→0

- Differentiation Of Function F ( x ) is denoted By ,

F'( x )  Or   df (x )

                    dx

Geometric Interpretation Of Derivative

- Slope Of A Graph At a Point Is called Derivative of a function at that point .

- Change Of one Quantities with respect to other quantities 

This is mainly two Geometric interpretation Of Derivatives.

   Some Important Questions 

Question 01 )

Find the derivative at x = 2 of the function F ( x ) = 3x 

Solution : View On this Page 

( Question 01 )

Question 02 )

F ( x ) = 2x² + 1 , be a real value function then find F' ( 2 ) .

Solution : View On this Page 

( Question 02 )

Question 03 ) 

Find the derivative of the function F ( x ) = 2x² + 3x - 5 at x = 1 

Also , Prove F' ( 0 ) + 3 F' ( -1 ) = 0

Solution : View On this page .

( Question 03 )

Question 04 ) 

Find the derivative of Sinx at x = 0 

Solution : View On this Page 

( Question 04 )

This is Complete Notes of Lecture 02 Differentiation

Click For Download 

Some Important Trigonometry Function 

sin(x+y) = sin(x)cos(y)+cos(x)sin(y)

cos(x+y) = cos(x)cos(y)–sin(x)sin(y)

sin(x–y) = sin(x)cos(y)–cos(x)sin(y)

cos(x–y) = cos(x)cos(y) + sin(x)sin(y)

And Also ,

SinA + SinB  =  2sin (A + B )/2 Cos( A - B )/2

SinA  - SinB  =  2Cos (A + B )/2 Sin( A - B )/2

CosA + CosB = 2Cos(A + B )/2 Cos( A - B )/2

CosA - CosB  = - 2Sin (A + B )/2 Sin( A - B )/2

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