Applied Mathematics - ll : Differentiation | Chapter 02 | Lecture 06 Notes For Polytechnic.
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Applied Mathematics - ll : Differentiation|Chapter 02 | Lecture 06 Notes For Polytechnic
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| ( Lecture 06 ) |
Hey Everyone, How are you ... Today I will tell you How to Differentiate Polynomial Function, Modulus Function & Trigonometry Function also Algebra Of Differentiation Such as addition, Subtraction, Product & Quotient Which is lecture 06 of Chapter 02 Differentiation Of Applied Mathematics 2
Lecture - 05 ( Topics ) :
1 ) Algebra Of Derivative Of Function
a ) Addition
b ) Subtraction
c ) Product
d ) Quotient
2 ) Some Important Formulas
3 ) Differentiation Of Polynomial Function, Modulus Function & Trigonometry Function .
4 ) Lecture Related Questions
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| ( Topic Overview ) |
Algebra Of Derivative Of Function
- The Algebra Of Derivative of function defines the addition, Subtraction, Multiplication & Division Of Differentiation.
- Let F & G be two function such that their derivative are defined in a common domain
1 ) Derivative of Sum Of two Function Is sum of the derivative Of The Function.
d { F (x ) + G (x ) = d F (x ) + d G (x )
dx dx dx
2 ) Derivative of Difference Of two Function Is difference of the derivative Of The Function.
d { F (x ) + G (x ) = d F (x ) + d G (x )
dx dx dx
3 ) Derivative of Product Of two Function Is given by the following product rule.
d { F (x ).G (x ) = d F (x ).G (x ) + d G (x ).f(x)
dx dx dx
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| ( Algebra of Differentiation ) |
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| ( Algebra Of differentiation ) |
Important Formulas
( 1 ) d ( C ) = 0
dx
( 2 ) d ( X^n ) = nX^n-1
dx
( 3 ) d ( e^x ) = e^x
dx
( 4 ) d ( a^x ) = a^xloga
dx
( 5 ) d ( logx ) = 1/x
dx
( 6 ) d ( Sin x ) = Cos x
dx
( 7 ) d ( Cos x ) = - Sin x
dx
( 8 ) d ( tan x ) = Sec²x
dx
( 9 ) d ( Cot x ) = - Cot²x
dx
( 10 ) d ( Sec x ) = Sec x . tan x
dx
( 11 ) d ( Cosecx ) = - Cosex .Cot x
dx
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| ( Important Formulas ) |
Some Important Question
Question 01 ) Differentiate the following function w.r.t x
( a ) F ( x ) = Sin x + a^x
Solution : View On This Page
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| Q1 ( a ) |
( b ) F ( x ) = x ³ + cosx + e^x
Solution : View On This Page
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| Q1 ( b ) |
( c ) F ( x ) = Log base 10 X
Solution : View On This Page
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| Q1 ( c ) |
( d ) F (X ) = Log x + e^x +tan x
Solution : View On This Page
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| Q1 ( d ) |
Question 02 ) Differentiate The Following Function w.r.t x
( a ) ax² + bx +c
✓ x
Solution : View On This Page
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| { Question 02 (a) } |
( b ) ( X² + 1/X² )³
Solution : View On This Page
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| { Question 02 (b) } |
Question 03 ) Find Differentiation , If y = Sin ( x + a ) / Sin x.
Solution : View On This Page
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| { Question 03 } |
Question 04 ) Find Derivative Of the following for given ,
Y = x |x |; when x < 0 & 0< x
Solution : View On This Page
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| ( Question 04 ) |
Question 05 ) Write the value of Function Derivative Of |✓x - 1 |+ | x - 5 | ,When 1< x & x< 5 .
Solution : View On This Page
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| ( Question 05 ) |
Question 06 ) If y = 1+ x + x²+ x³ + ...
1! 2! 3!
Prove That : dy = y
dx
Solution : View On This Page
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| ( Question 06 ) |
Lecture Related Notes
Question 01 ) Differentiate the following function with w.r.t to x .
( a ) log base 10
Ans - 1 / x log x
( b ) e^x + Sin x + log x
Ans - e^x + Cosx + 1/x
( c ) 9 ( 3^ x )
Ans - 9 ( 3^x log 3 )
Question 02 ) Find dy If y = ( x + 1/x )
dx
( ✓x + 1/✓x ) .
Question 03 ) Differentiate X²|x| when x < 0.
Answer ) -3x²
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