1. ## easy derivative question

Hey guys, for an economics class actually, how would you derivate this ?

TC = 4(30 - Q2)2 + 5Q22 - (30 - Q2)Q2

2. ## Re: easy derivative question

TC = 4(30 - Q2)2 + 5Q22 - (30 - Q2)Q2
derivative w/respect to what variable?

What is TC? is that a single variable or a product? what is Q?

are there exponents in your expression? use the caret symbol like so ... x^2 is x squared ... (x^2 + 2)^2 is the quantity (x^2 + 2) squared.

what does 5Q22 mean?

do you know the power & chain rules for derivatives?

3. ## Re: easy derivative question

Hey guys, for an economics class actually, how would you derivate this ?
TC = 4(30 - Q2)2 + 5Q22 - (30 - Q2)Q2
I think that you mean "derive". Also that there is a mixture of subscripts and superscripts(exponents).
If that is ether the case or not the case please revise the post to make it perfectly clear what you mean.

4. ## Re: easy derivative question

Hey guys, for an economics class actually, how would you derivate this ?

TC = 4(30 - Q2)2 + 5Q22 - (30 - Q2)Q2

Sorry this is what I meant, did not realise the typos, this is the function that I need to derive:
Total Cost = 4(30 - Q)^2 + 5Q^2 - (30 - Q)Q

5. ## Re: easy derivative question

Let Total Cost $\displaystyle = C = 4(30 - Q)^2 + 5Q^2 - (30 - Q)Q$.
$\displaystyle \frac{dC}{dQ} = 4\cdot 2(30-Q)(-1) + 5\cdot 2Q - [(30-Q)(1) + Q(-1)] = 20Q -270$

Note: Give some time to load properly, run Tex and compile the equation.

6. ## Re: easy derivative question

Equivalently, C= 4(30- Q)^2+ 5Q^2- (30- Q)Q= 3600- 240Q+ 4Q^2+ 5Q^2- 30Q+ Q^2= 3600- 270Q+ 10Q^2
so dC/dQ= -270+ 20Q.