Basic Rules
Because the derivative is a limit, many of the rules of limits
apply to the derivative:

(cf (x))' = c(f'(x)) where c is a constant. This says that the derivative of a scalar multiple of a
function is equal to the derivative of the function multiplied by the scalar multiple.

(f (x) + g(x)) = f'(x) + g'(x). The derivative of a sum of two functions is equal to the
sum of the individual derivatives.
The Power Rule
This is a powerful way of finding the derivative of a polynomial
function. It says:
where n is a real number. For example,
The Product Rule
If f and g are two differentiable functions, then
(fg)' = f'g + g'f.
For example,
The Quotient Rule
If f and g are two differentiable functions, then
For example,