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.

deriv2

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:

daum_equation_power_rule

For n = 0 we should apply constant rule:

daum_equation_constant_rule

Product Rule

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

In this case we can apply the below formula:

daum_equation_product_rule

Here goes an example with three functions:

daum_equation_prod_rule_2

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.

daum_equation_quotient_rule_1

So the derivative will be equal to:

daum_equation_quotient_rule_2

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:

daum_equation_chain_rule

For example, what is derivative of daum_equation_chain_rule_3:

daum_equation_chain_rule_2

 

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