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Product rule

With the product rule you can calculate the derivative of a product of two functions

This formula is stated quite unclear.

 


Explanation

We start with the functions f (x) en g (x). In the definition of the derivative we substitute these functions

By adding and subtraction the term  in the numerator we get

The limit of a sum is the sum of the limits, so

As h→0 the two fractions describe the derivatives f ′(x) and g ′(x). The function f (x) is differentiable, so f (x + h) → (x)

You can guess what the product of 3 functions will look like.

 


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