Power Rule, Product Rule, Quotient Rule and Chain Rule

Recently, I had a need to use derivative. So I decided to make this short overview of the four fundamental rules to refresh and recall my knowledge in evaluating derivatives. The overview doesn’t contain any proves, it’s just a reference where you and I can quickly find differentiation rules that can be applied on derivatives. Moreover, I skipped some other rules such as sum or difference rule.

Power Rule

The power rule says: For n = 0 we should apply constant rule: Product Rule

Let say we want to take a derivative of a product of two functions and .

In this case we can apply the below formula: Here goes an example with three functions: I think the idea is very simple so we can go ahead with the next rule.

Quotient Rule

The quotient rule can be applied in case if you want to take a derivative of a function that is quotient of two other functions. So the derivative will be equal to: By the way you can use product rule instead of quotient rule.

Chain Rule

The chain rule is a rule for computing derivative of the composition of two or more functions.

The formula of the chain rule can be expressed as: For example, what is derivative of : 