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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.

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

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.