From the course: Complete Guide to Calculus Foundations for Data Science
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Product rule
From the course: Complete Guide to Calculus Foundations for Data Science
Product rule
- [Instructor] Let's take a look at the product rule. Note that this rule is similar to the quotient rule, but they will be discussed separately due to their complexity and importance. Let's start off with the definition. The product rule states the derivative of a product of functions only works if each of the functions are differentiable individually. If they are differentiable, then the product rule states the derivative of the functions h of X equals the function f of x multiplied by the function g of x. Then the derivative of h prime of x equals f prime of x multiplied by g of x, plus f of x multiplied by g prime of x. You may wonder why you don't just multiply the two functions together. For example, how you would with the sum and difference rules where you simply add or subtract them from each other. Let's look at an example as to why this does not work. Let's say you have the function f of x and it is equal to x squared multiplied by x cubed. If you've simply multiplied these…
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