# How do you find the derivative of #f(x) = 3#?

##### 1 Answer

#f'(x) = 0#

#### Explanation:

The derivative of a constant is always

**1. Basic Principles**

For

#f(x + h) = c#

(Normally you would replace every instance of

#f'(x) = lim_(h->0) (f(x+h) - f(x))/h = lim_(h->0)(c-c)/h#

# = lim_(h->0) 0 = 0# for all values of#c#

**2. Power Rule**

#f(x) = c*1 = c*x^0#

The Power Rule states that for all

#f'(x) = nx^(n-1)#

For

#f'(x) = c*nx^(n-1) = c*(0)x^(-1) = 0# for all values of#c#

Another way to view this is by graphing the function of

graph{3*x^0 [-10, 10, -5, 15]}

The derivative of a function can also be viewed as the slope of that function at a certain point in time. Since a constant value is graphed as a straight line and never moves up or down, the slope will always be