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:
|xn = nxn-1|
where n is a real number. For example,
|x4 = 4x3|
The Product Rule
If f and g are two differentiable functions, then (fg)' = f'g + g'f. For example,
|(3x)( = 3 +3x(x-)|
The Quotient Rule
If f and g are two differentiable functions, then