# How do you find the derivative of #g(x) = -4x + 5 #?

##### 1 Answer

#### Explanation:

There are two ways to go about this. The first, I will be using the rules of derivatives. The second, I'll be showing by first principles.

**Method 1: Rules of Derivatives**

There are two rules we'll be using to solve this. The first is the derivative of a polynomial, which says:

The highest power we have is 1, so by bringing that down, we remove the x since

By applying both rules, we can get:

**Method 2: First Principles**

This method can be used to take the derivative of literally any function. A derivative is the instantaneous rate of change at a point, and we want the function for it. So we'll apply the rate of change formula (

So let's plug in our function:

Let's expand this.

And let's get the like terms together:

And as that approaches 0, we just get

Now, you have two methods of finding the derivative. One for polynomials, one for any other function.