Differential Calculus – The Rules of Differentiation


The Product Rule:
product rule

We use the Product Rule when we have products of two or more functions. In case of three functions, we take any two functions as as and differentiate the third as so on hence, forming three terms in the sum.

There is also a quotient rule for derivatives of functions in the form u/v but, we will stick with the product rule for the form u/v by treating (1/v) as a function of x.
But we should be familiar with the quotient rule too. According to the quotient rule:
quotient rule
Now, if we are dealing with composite functions, we need to use the chain rule to find their derivatives which is stated below:
chain rule
Now, using the above rules and the table of derivatives in the previous post, we can find the derivative of any function and combination of functions (applying the rules as needed).


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