# How do you find the derivative of #f(x)=x^2-5x+3#?

##### 1 Answer

#### Explanation:

The **derivative** of a function is the **instantaneous rate of change** of the function at a given point. But we have a function, so we want to find the rate of change throughout. We have two ways of doing this, and I'll show you both ways.

**Method 1: The Power Rule**

This method only works for polynomials (

So we can apply this to your function. But we also have a constant. Remember that adding or subtracting a constant yields only a vertical shift, not a stretch. Therefore, it has no effect on the rate of change, so we can also say:

We can use these two rules together to get the answer:

**Method 2: First Principles**

First Principles is a method that allows you to take the derivative of any function. It comes from the slope formula (

So let's plug in your function:

Since we can't divide by 0, we need to get the h out of the denominator. So let's expand the binomial.

And let's combine all the like terms (cancelling out most of the x values):

Now, every term as an h somewhere in it. So we can divide by h:

And now as the limit approaches 0, 2h reaches 0, and therefore, we are left with the final answer: