Applied Mathematics - ll : Differentiation|Chapter 02 | Lecture 07 Notes For Polytechnic

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Applied Mathematics - ll : Differentiation|Chapter 02 | Lecture 07 Notes For Polytechnic

( Lecture 07 )

Hey Everyone, How are you ... Today I will tell you How to Derivative Of Function By using product & Quotient rule Which is lecture 07 of Chapter 02 Differentiation Of Applied Mathematics 2 

Lecture - 04 ( Topics ) :

1 ) Differentiation Of  Function By Using Product & Quotient Rule 

2 ) Most Important Questions Related To Product Rule.

3 ) Most Important Questions Related To Quotient Rule.

4 ) Lecture Related Questions.

( Overview Of lecture )

 # Product Rule ;-

Let F (x ) & g( x ) be two Function Then differentiation ,

  d  { F(x).g(x) } = F(x) d g (x) + g(x) d f(x)

dx                                  dx.                   dx

Or ,

     (  uv )' = u'v +uv'

- Notes this product Formula 

Product Formula 

# 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 ) = - Cot²x

        dx

( 10 ) d ( Sec x ) = Sec x . tan x

         dx

( 11 ) d ( Cosecx ) = - Cosex .Cot x

         dx

Questions Related To Product Rule

Question 01 ) Differentiate w.r.t, x 

Y = X Sin X 

Solution : View On This Page 

( Question 01 )

Question 02 ) Differentiate ( X + Cosx ) ( x - tanx ) , w.r.t x

Solution : View On This Page 

( Question 02 )

Question 03 ) Find dy , If y = e^x sin x  + x³ Cos X.           dx

Solution : View On This Page 

( Question 03 )

Question 04 ) Find dy , If y = x⁴ e^x secx .                         dx

Solution : View On This Page 

( Question 04 )

 # Quotient Rule :-

Let F (x ) & G (x ) are two function .

Then , 

  d  ( f (x) } = g(x) f'(x) - f(x) g'(x) 
 dx { g(x) }            { g(x) }²

- Important Rule 

 Question Based On Quotient Rule

 

Question 01 ) Differentiate x + Cosx

With respect To x                     tanx 

Solution : View On This Page 

( Question 01 )

Question 02 ) Differentiate 1 + tan x

                                                     1 - tanx 

With respect to x 

Solution : View On This Page 

( Question 02 )

Question 03 )  Find dy  If : y = 2X + 3 
                                    dx                X² + 5

Solution : View On This Page 

( Question 03 )

Differentiation Lecture 07 Notes ;

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