Rules for derivatives

Constant Rule: The derivative of a constant is 0. That is f(x) = c is a horizontal line, with 0 slope. Alternatively, you can think of c as a function which never changes, so its rate of change is zero.

 Scalar Multiple Rule:  The derivative of a constant times a function is the constant times the derivative of the function.

Sum Rule: The derivative of the sum (or difference) of two functions is the sum (or difference) of their derivatives.

Product Rule: The derivative of a product is "the first factor times the derivative of the second plus the second factor times the derivative of the first".
(see also the annotated version)

Quotient Rule: The derivative of a quotient is "the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, over the denominator squared".
(see also the annotated version)

Chain Rule: The derivative of a function of u with respect to x is the derivative of the function with respect to u times the derivative of u with respect to x.

Power Rule: The derivative of u to the nth power is n times u to the power decreased by 1 (or the new power is n-1) times the derivative of u with respect to x.

 Absolute Value Rule: The derivative of the absolute value of u is the derivative of u multiplied by the ratio of u over the absolute value of u, wherever u is not equal to 0.
, wherever u(x) ≠ 0.