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Thread: easy derivative question

  1. #1
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    easy derivative question

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

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

    Thanks in advance!
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  2. #2
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    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?
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  3. #3
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    Re: easy derivative question

    Quote Originally Posted by haderach8 View Post
    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.
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    Re: easy derivative question

    Quote Originally Posted by haderach8 View Post
    Hey guys, for an economics class actually, how would you derivate this ?

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

    Thanks in advance!
    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
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  5. #5
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    Re: easy derivative question

    Let Total Cost = C = 4(30 - Q)^2 + 5Q^2 - (30 - Q)Q .
    \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.
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  6. #6
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    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.
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