Blog #4: Derivatives

Hello! My name is Professor Bazerman and today I will be teaching you how to find the derivative of a function.

When you hear the word derivative, it can sound intimidating. I know when I was first introduced to the concept, I didn't know what I was getting myself into, but it is really simple.

Before I teach you how to actually solve for the derivative, we need to understand why we even need to take the derivative of a function. For instance, we can look at a real life example...

Out in Topeka, Kansas there is a small factory that is producing computers to sell. They are trying to figure out how much it will cost them to produce 100 computers to sell to various companies, so they can make sure that they are covering all costs of production, while still making a profit.

We can determine this by evaluating the following function:
R(q)= 2,000q^3-4q^2

In order to find out how much it would cost for a specific number of items, we would need to take the derivative of this function...

So here's what we have to do:

Step 1:
Multiply the exponent by the base number:
2,000*3= 6,000

Step 2:
Then, you subtract 1 from the exponent:
3-1=2

Step 3:
You combine your solutions:
6,000q^2

Step 4:
Repeat the same steps again for the second part of the function:
4*2=8
2-1=1 -->8q

Step 4:
You now have found the derivative of your revenue function:
R'(q)=6,000q^2-8q
This is now the marginal revenue function.

Now, let's say we want to find out how much it would be to sell 100 computers.

We set q=100, and plug it into our derivative function:


R'(100)= 6,000(100)^2-8(100)
R'(100)= $59,999,200

$59,999,200 would be the total cost to produce 100 computers. 

See, was that so hard? Trying to find the derivative of a function can be intimidating, but in reality, it is pretty simple!

That's all for now! Hope this was helpful!!