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Basic Laws of Differentiation

  • Scalar multiple rule
     
    Let f (x) and g (x) be any two functions of x. Then, Description: 72749.pngDescription: 72755.png where, c is any constant

    Example
    Description: 78920.png
    Solution
    Description: 72767.png
    =Description: 78937.png
     
    = 6x
  • Sum and difference rule
     
    Description: 72785.png
    Example
    Description: 72797.png
    Solution
    Description: 72803.png
     
    Description: 72809.png  
  • Product rule
     
    Description: 72815.png
     
    Description: 72827.png(1st function × 2nd function)
     
    = (1st function × differentiation of 2nd function) + (2nd function × differentiation of 1st function)
     
    Example
    Description: 72833.png
    Solution
    Description: 72839.png
     
    Description: 72845.png
  • Quotient rule
     
    Description: 72851.png
     
    Description: 72863.png

Example
Description: 72869.png
Solution
Description: 72875.png
Description: 72881.png 
 
 
Example
Description: 79080.png
Solution
Description: 72893.png

 

Example
Description: 72899.png
Solution
Description: 72905.png
Description: 79118.png 

 
Example
Description: 72923.png
Solution
Description: 72929.png
Description: 72935.png 

 

Example
Description: 92563.png
Solution
If u and v are two functions of x, then we know that
Description: 72941.png
In the given expressionDescription: 72947.png 
Description: 72953.png 
Description: 79170.png 

 
Example
Description: 72959.png
Solution
If u and v are two functions of x, then we know that
Description: 72965.png
In the given expressionDescription: 72971.png 
Description: 72977.png 

Derivative of a Function

Let y = f (u), where u = g(x)

ThenDescription: 72983.png
 

Example
Description: 72989.png
Solution
In the given expressionDescription: 72995.png
Description: 73001.png 
Description: 79247.png 





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