Thread: Need help differentiating an expression. Answer is given just unsure of the steps.

Hello, this problem states to differentiate the expression with respect to q. I am not sure of the steps taken to get the final result.

This is an economics problem differentiating the variable cost function to get the marginal cost function.

So you want to differentiate:

with respect to q?

In which case, we have:



=

But the (everything except the ) is just constant. It's a stable value, like 4 or 7 - it isn't a variable.

For the sake of simplicity, I'm going to let

When we differentiate with respect to , we get: .

When we differentiate with respect to , we get:

We have:

So, differentiating, we get:

Then, slipping c back in as , we have:



and which is where that number arises.