The product rule in calculus is used to take the derivative of a function that is the multiplication of two or smaller functions. In other words, if a function f(x) is a product of functions if it can be written as g(x)h(x), and so on. Consider the following example.
This function is a product of two smaller functions.
Here f(x) is the product or multiplication of two smaller functions.There can also be a situation where our f(x) is the product of three or more smaller functions:
This function is the product of three smaller functions.
The derivative of such function is found with the help of product rule in calculus.
The formula of the product rule for the product of two functions is stated below:
The product rule formula.
If the function is a product of three function, the formula becomes the following:
The product rule formula for the product of three functions.
For finding the derivative of a function which is the product of two functions, the derivative of the first function is multiplied to the second function and added to the derivative of the second multiplied by the first function. Same pattern is followed in case of product of three functions derivative of one function is multiplied keeping other functions as it is and then summing up each term.
Following is an example of finding out the derivative of a function which is a product of two function using the product rule
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