

Differential calculus  derivatives 
Differentiation
rules 
The
derivative of the sum or difference of two functions 
The
product rule 
A
constant times a function rule 
Derivatives of functions, examples 
The
quotient rule 
The
derivative of the tangent function, use of the quotient rule 
The
derivative of the cotangent function, use of the quotient rule 







Differentiation
rules 
The
derivative of the sum or difference of two functions 
The
derivative of the sum or difference of two differentiable functions
equals the sum
or difference of their derivatives,
written 


The
product rule 
The
derivative of the product of two differentiable functions is
equal to, the first function times the derivative of the second
plus the second function times the derivative of the first, 


A
constant times a function rule 
The
derivative of a constant times a function is equal the constant
times the derivative of the function, where
the
constant c
can be any real number or expression that does not contain the
variable, 


Derivatives of functions, examples 
Example: 
Find
the derivative of the function f
(x)
= m x
+ c. 

Solution: 




Example: 
Find
the derivative of the function 


Solution: 




Example: 
Find
the derivative of the function 


Solution: 




Example: 
Find
the derivative of the function 


Solution: 




The
quotient rule 
The
derivative of the quotient of two differentiable functions is,
the denominator times the derivative of the numerator
minus the numerator times the derivative of the denominator all
divided by the denominator squared,
written 


The
quotient rule used to differentiate an expression where a
constant is divided by a function, 


The
derivative of the tangent function, use of the quotient rule 
Since 

then,
we obtain the derivative of the tangent function by using
the quotient rule, so 



Therefore,
if

f(x)
= tan x 
then 




The
derivative of the cotangent function, use of the quotient rule 
Since 

then,
we obtain the derivative of the cotangent function by
using the quotient rule, so 



Therefore,
if

f(x)
= cot x 
then 













Calculus contents
C 



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