Differentiation Rules

    Here is a summary of the basic differentiation rules taking into account the chain rule.

Proposition (Differentiation Rules) If and are differentiable functions and is a constant, then

Example (Differentiation Rules) Find the derivatives of the function  

    Solution. Using the chain rule and the quotient rule, we determine,



which simplifies to





Example (Differentiation Rules) Find the derivatives of the function  

    Solution. Using the chain rule and the quotient rule, we determine,
    


which simplifies to





Example (Differentiation Rules) Find the derivatives of the function  

    Solution. Using the chain rule and the formula we determine





Example (Differentiation Rules) Find the derivatives of the function  

    Solution. Using the chain rule,







Example (Differentiation Rules) Find the derivatives of the function  Show that and

    Solution. Using the differentiation rule we have,



Using we also find,













Example (Differentiation Rules) Find the derivatives of the function  

    Solution. Using the quotient rule with the chain rule, we determine,



whcih simplies to

    
    

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Cite this as:
Differentiation Rules
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/differentiation-rules.html