Differentiation rules are rules (actually, theorems) used to compute the derivative of a function in calculus. In what follows, all functions are assumed to be differentiable.
Derivative of a Constant: If is a constant function then .
Sum Rule: If then .
Product Rule: If then .
Quotient Rule: If then .
Chain Rule: If then .
Power Rule: If then . For integer this is just a consequence of the product and quotient rules and induction, but it can also be proven for all real numbers , e.g. by using the extended Binomial Theorem.
Derivatives of Trig Functions
Derivative of Sine If , then .
Derivative of Cosine If , then .
Derivative of Tangent If , then . Note that this follows from the Quotient Rule.