Differentiation Of Different Function | Chapter 03 | Lecture 01 Notes For Polytechnic
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Applied Mathematics - ll : Differentiation Of Different Function|Chapter 03 | Lecture 01 Notes For Polytechnic
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| ( Lecture 01) |
Hey Everyone, How are you ... Today I will tell you How to Derivative Of Inverse Trigonometry Function, Which is lecture 01 of Chapter 03 Differentiation Of Different Function Applied Mathematics 2
Lecture - 01 ( Topics ) :
1 ) Differentiation Of Inverse Trigonometry Function
2 ) Some Important Questions.
3 ) Lecture Related Questions.
Differentiation Of Inverse Trigonometry function by ;-
( 1 ) d ( Sin-¹x ) = 1 /( ✓ 1 - x² )
dx
( 2 ) d ( Cos-¹x ) = -1 / ( ✓ 1- x² )
dx
( 3 ) d ( tan-¹x ) = 1 / ( 1 + x² )
dx
( 4 ) d ( Cot-¹ x ) = - 1 / ( 1 + x² )
dx
( 5 ) d ( Sec-¹x ) = 1 / ( x ✓ x² - 1 )
dx
( 6 ) d ( Cosec-¹x ) = - 1 / ( x ✓ x² - 1 )
dx
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| ( Theorem ) |
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| ( Theorem ) |
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| ( Theorem ) |
Questions Related To Inverse Trigonometry Function ✔️
Question 01 )
Differentiate y = Sin-¹ ( x³ ) w.r.t x,
Solution : View In This Page
( Question 01 )
Question 02 )
Solution : View On This Page
( Question 02 )
Question 03 )
Differentiate y = e^( Cos-¹✓ 1 - x² ), w.r.t x.
Solution : View On This Page
( Question 03 )
Question 04 )
Differentiate y = Sin-¹ { a + b Cos x / b + a Cosx } , w.r.t x.
Solution : View On This Page
( Question 04 )
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| (Question 04 ) |
Question 05 )
If y = x Sin-¹x / ( ✓ 1 - x² ) + log ✓ 1 - x² , Prove that x²Sin-¹x / ( 1 - x² ) ^3/2 .
Solution : View On This Page
( Question 05 )
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| ( Question 05 ) |
Differentiation Lecture 08 Notes ;
Important Trigonometry Formulas ;
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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