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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