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Math Help - Can someone explain to me the order of operations for this derivate?

  1. #1
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    Can someone explain to me the order of operations for this derivate?

    Or better yet, the OOO for derivates with multiple steps. here is my example:

    (5x-5)^2(4-x^3)^4

    But what happens if I have to use the chain rule, product rule, and the quotient rule? What order do I do them in? Say I had the same problem but slightly altered:

    [(5x-5)^2(4-x^3)^4]/3x

    Thanks in advance!
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  2. #2
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    Quote Originally Posted by a13firman View Post
    Or better yet, the OOO for derivates with multiple steps. here is my example:

    (5x-5)^2(4-x^3)^4

    But what happens if I have to use the chain rule, product rule, and the quotient rule? What order do I do them in? Say I had the same problem but slightly altered:

    [(5x-5)^2(4-x^3)^4]/3x

    Thanks in advance!
    I'd use the quotient rule first and then use the product rule on the numerator u
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    is that the only way to do it? or does it not matter?
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    Quote Originally Posted by a13firman View Post
    is that the only way to do it? or does it not matter?
    That is as good a way as any. What other way did you have in mind?
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    I just mean if you tried it using one of the other rules first would it give you a different answer?
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  6. #6
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    Quote Originally Posted by a13firman View Post
    I just mean if you tried it using one of the other rules first would it give you a different answer?
    If the rules are used in a valid way, you must get the same answer. But I don't see how you could correctly do it too much differently to what has already been suggested.
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    So for the second equation I wrote, I use the quotient rule first, then the chain rule, then the product rule? Or quotient, product, then chain? The other guy who answered left out chain which I think needs to be used, but correct me if I am wrong.

    Thanks for the help!
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  8. #8
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    Quote Originally Posted by a13firman View Post
    So for the second equation I wrote, I use the quotient rule first, then the chain rule, then the product rule? Or quotient, product, then chain? The other guy who answered left out chain which I think needs to be used, but correct me if I am wrong.

    Thanks for the help!
    1. To differentiate [(5x-5)^2(4-x^3)^4]/3x you should start with the quotient rule.

    2. To get the derivative of the numerator you should use the product rule.

    3. To get the derivative of each member of the product you might need to use the chain rule.

    That is the logical order I would do things in.
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