What is Differentiation?
Differentiation can be defined as a derivative of independent variable value and can be
used to calculate features in an independent variable per unit modification.
Let,y = f(x), be a function of x.
dy
Then, the rate of change of “y” per unit change in “x” is given by, or y’
dx
Rules of Derivative Formula
d
1. Constant rule : ( c )=0
dx
d d
2. Constant multiple rule ( cf ( x))=c ( f (x) )
dx dx
d n
3. Power Rule ( x )=n x n−1
dx
d d d
4. Sum Rule ( f ( x ) + g(x ) )= ( f (x) ) + ( g (x) )
dx dx dx
d d d
5. Difference Rule ( f ( x )−g ( x) ) = ( f (x ) )− ( g( x ))
dx dx dx
d
6. Product Rule ( f ( x ) . g (x) ) =f ( x ) . g' ( x ) + g ( x ) . f ' x
dx
( )
' '
d f ( x) g ( x ) . f ( x )−f ( x ) . g ( x )
7. Quotient Rule =
dx g( x ) g( x )
2
Differentiation of log and exponential functions
d x
(e ) = ex
dx
Differentiation can be defined as a derivative of independent variable value and can be
used to calculate features in an independent variable per unit modification.
Let,y = f(x), be a function of x.
dy
Then, the rate of change of “y” per unit change in “x” is given by, or y’
dx
Rules of Derivative Formula
d
1. Constant rule : ( c )=0
dx
d d
2. Constant multiple rule ( cf ( x))=c ( f (x) )
dx dx
d n
3. Power Rule ( x )=n x n−1
dx
d d d
4. Sum Rule ( f ( x ) + g(x ) )= ( f (x) ) + ( g (x) )
dx dx dx
d d d
5. Difference Rule ( f ( x )−g ( x) ) = ( f (x ) )− ( g( x ))
dx dx dx
d
6. Product Rule ( f ( x ) . g (x) ) =f ( x ) . g' ( x ) + g ( x ) . f ' x
dx
( )
' '
d f ( x) g ( x ) . f ( x )−f ( x ) . g ( x )
7. Quotient Rule =
dx g( x ) g( x )
2
Differentiation of log and exponential functions
d x
(e ) = ex
dx
