How do you use the definition of a derivative to find the derivative of #f(x)=-3x#?
The derivative is equal to
Strictly using the limit definition of the derivative:
The limit definition of the derivative looks like this:
If we replace
Simplifying, we get:
So, the derivative of
Using the meaning of the derivative:
We know that the derivative means the rate of change of the function. Graphically, this means that the derivative is the slope of the graph of that function.
We can figure out the slope of this line by remembering the general formula for a linear equation:
In our case,