Differentiation | Chapter 02 | Lecture 08 Notes For Polytechnic
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Applied Mathematics - ll : Differentiation|Chapter 02 | Lecture 08 Notes For Polytechnic
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| ( Last lecture ) |
Hey Everyone, How are you ... Today I will tell you How to Derivative Of Function By using Chain rule Which is lecture 08 of Chapter 02 Differentiation Of Applied Mathematics 2
Lecture - 08 ( Topics ) :
1 ) Differentiation Of Function By Using Chain Rule
2 ) Most Important Questions Related To Chain Rule.
3 ) Lecture Related Questions.
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| ( Overview ) |
- Differentiation Of function by chain rule ;-
- Let F (y ) & g( x ) be two Function Then differentiation ,
And , z = F (x ) & y = g( x )
Then,
dz/dx = dz/dy × dy/dx
- Notes this product Formula
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| Chain rule |
- Important Formula ;
( 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 ) = - Cosec²x
dx
( 10 ) d ( Sec x ) = Sec x . tan x
dx
( 11 ) d ( Cosecx ) = - Cosex .Cot x
dx
Questions Related To Chain Rule ✔️
Question 01 )
Differentiate log ( sinx ) w r.t x .
Solution : View In This Page
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| Question 01 |
Question 02 )
Differentiate y = Sin2x , w.r.t x.
Solution : View On This Page
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| Question 02 |
Question 03 )
Differentiate y = log Sinx² , w.r.t x.
Solution : View On This Page
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| Question 03 |
Question 04 )
Differentiate y = ✓ x² - 4x +4 , w.r.t x.
Solution : View On This Page
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| ( Question 04 ) |
Question 05 )
If Y = { x + ✓ a² + x ² } . Prove That dy/dx = ny/ ✓ x² + a²
Solution : View On This Page
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| ( Question 05 ) |
Question 06 )
If y = ✓ a² - x² prove that ydy/dx + x = 0
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| ( Question 06 ) |
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| ( Question 07 ) |
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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