ROYAL ACADEMY TUTORS
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Rules of differentiation
Power Rule
( ) ( )
Product Rule
Used to differentiate a “product” of two different functions.
( ) where u and v are both functions of x.
( ) : where du and dv are the derivatives of u and v with respect
to x, respectively.
Quotient Rule
Used to differentiate a “quotient” or a fraction of two functions.
( ) : where u and v are both functions of x.
( )
du and dv are the derivatives of u and v with respect to x, respectively.
The Chain Rule
Used to differentiate a function of a function or a multiple of these.
By making the necessary substitutions, a chain of derivatives is used to
compute the derivative of the particular function, for example,
If ( ) ( ) ( ) then
( )
Notice how the du and dv terms will disappear, by cancelling each other out, to
yield the desired derivative, .
Providing World Class Tuition Fit for Kings & Queens
Directors
Mr. Kingston Mangwadu – B. Sc. (Hons) Civil Engineering III (University of Zimbabwe) Contact: +27 83 427 5621
Mrs. T. Lethebe – B. Com. Business Management (Central University of Technology) Contact: +27 73 028 2253 Page 1
Empowering you to conquer your world
Rules of differentiation
Power Rule
( ) ( )
Product Rule
Used to differentiate a “product” of two different functions.
( ) where u and v are both functions of x.
( ) : where du and dv are the derivatives of u and v with respect
to x, respectively.
Quotient Rule
Used to differentiate a “quotient” or a fraction of two functions.
( ) : where u and v are both functions of x.
( )
du and dv are the derivatives of u and v with respect to x, respectively.
The Chain Rule
Used to differentiate a function of a function or a multiple of these.
By making the necessary substitutions, a chain of derivatives is used to
compute the derivative of the particular function, for example,
If ( ) ( ) ( ) then
( )
Notice how the du and dv terms will disappear, by cancelling each other out, to
yield the desired derivative, .
Providing World Class Tuition Fit for Kings & Queens
Directors
Mr. Kingston Mangwadu – B. Sc. (Hons) Civil Engineering III (University of Zimbabwe) Contact: +27 83 427 5621
Mrs. T. Lethebe – B. Com. Business Management (Central University of Technology) Contact: +27 73 028 2253 Page 1
