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    How would you differentiate y = 6x(1 + x^2 )^2

    I'm not sure in what situation you use chain rule and in what situation you would use product rule?

    If it was y = 6(1 + x^2 )^2
    ..could I use chain rule?
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    (Original post by Peanut247)
    How would you differentiate y = 6x(1 + x^2 )^2

    I'm not sure in what situation you use chain rule and in what situation you would use product rule?

    If it was y = 6(1 + x^2 )^2
    ..could I use chain rule?
    You would use both

    Though, tbh, I would just multiply that out
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    (Original post by TenOfThem)
    You would use both

    Though, tbh, I would just multiply that out
    What do you mean you would use both?
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    (Original post by Peanut247)
    What do you mean you would use both?
    You have a product so you need to use the product rule

    One of the functions is a function of a function so that would need the chain rule
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    (Original post by Peanut247)
    How would you differentiate y = 6x(1 + x^2 )^2

    I'm not sure in what situation you use chain rule and in what situation you would use product rule?

    If it was y = 6(1 + x^2 )^2
    ..could I use chain rule?
    You can use whatever rule you like. y(x) = 6(1+x^2)^2 requires first the use of linearity of the derivative, to obtain y'(x) = 6 \dfrac{d}{dx} (1+x^2)^2, then you could use chain to get y'(x) = 6 \times 2 (1+x^2) \dfrac{d}{dx} (1+x^2).

    Alternatively, you could use product: y(x) = 6 (1+x^2) (1+x^2) means y'(x) = 6 (1+x^2) \dfrac{d}{dx}(1+x^2) + 6 (1+x^2) \dfrac{d}{dx} (1+x^2).

    (By the way, y(x) = 6x (1+x^2)^2 = \dfrac{d}{dx} (1+x^2)^3 by chain rule. It doesn't help here, but some problems are made easier if you know that the function in question is the derivative of something.)
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    (Original post by Smaug123)
    You can use whatever rule you like. y(x) = 6(1+x^2)^2 requires first the use of linearity of the derivative, to obtain y'(x) = 6 \dfrac{d}{dx} (1+x^2)^2, then you could use chain to get y'(x) = 6 \times 2 (1+x^2) \dfrac{d}{dx} (1+x^2).

    Alternatively, you could use product: y(x) = 6 (1+x^2) (1+x^2) means y'(x) = 6 (1+x^2) \dfrac{d}{dx}(1+x^2) + 6 (1+x^2) \dfrac{d}{dx} (1+x^2).

    (By the way, y(x) = 6x (1+x^2)^2 = \dfrac{d}{dx} (1+x^2)^3 by chain rule. It doesn't help here, but some problems are made easier if you know that the function in question is the derivative of something.)
    You seem to be differentiating a different question

    Then you are referencing integration rules ... Why?
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    (Original post by Peanut247)
    How would you differentiate y = 6x(1 + x^2 )^2

    I'm not sure in what situation you use chain rule and in what situation you would use product rule?

    If it was y = 6(1 + x^2 )^2
    ..could I use chain rule?
    Fairly sure you can use just use chain for the second one
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    (Original post by TenOfThem)
    You seem to be differentiating a different question

    Then you are referencing integration rules ... Why?
    No he has not. Please read OP fully.

    Also, he merely made a comment on the integration bit...noting that in this particular case it didnt help but can sometimes be useful in such a problem.
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    (Original post by Smaug123)
    You can use whatever rule you like. y(x) = 6(1+x^2)^2 requires first the use of linearity of the derivative, to obtain y'(x) = 6 \dfrac{d}{dx} (1+x^2)^2, then you could use chain to get y'(x) = 6 \times 2 (1+x^2) \dfrac{d}{dx} (1+x^2).

    Alternatively, you could use product: y(x) = 6 (1+x^2) (1+x^2) means y'(x) = 6 (1+x^2) \dfrac{d}{dx}(1+x^2) + 6 (1+x^2) \dfrac{d}{dx} (1+x^2).

    (By the way, y(x) = 6x (1+x^2)^2 = \dfrac{d}{dx} (1+x^2)^3 by chain rule. It doesn't help here, but some problems are made easier if you know that the function in question is the derivative of something.)
    But when I differentiate y= 6x(1+ x^2)^2 using chain rule and the product rule I get different answers..
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    (Original post by newblood)
    No he has not. Please read OP fully.

    Also, he merely made a comment on the integration bit...noting that in this particular case it didnt help but can sometimes be useful in such a problem.
    If you say so
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    (Original post by Peanut247)
    But when I differentiate y= 6x(1+ x^2)^2 using chain rule and the product rule I get different answers..
    Once again ... You need to use both but it would be better to multiply it out


    Can I check .... Since I have been told that I have misread

    You are differentiating 6x(1+x^2)^2 and none of those x are a multiplication sign ... Or ?
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    (Original post by TenOfThem)
    If you say so
    There is no need for attitude. Please try to be more helpful on the maths forum in future
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    (Original post by newblood)
    There is no need for attitude. Please try to be more helpful on the maths forum in future
    No attitude here ... We clearly have a different understanding of this thread ... As for your second point ... Are you serious
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    (Original post by TenOfThem)
    Once again ... You need to use both but it would be better to multiply it out


    Can I check .... Since I have been told that I have misread

    You are differentiating 6x(1+x^2)^2 and none of those x are a multiplication sign ... Or ?
    Yes none of them are multiplication signs sorry.
    So do you mean you would use chain regarding (1+x^2)^2 within the product rule?
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    (Original post by Peanut247)
    Yes none of them are multiplication signs sorry.
    So do you mean you would use chain regarding (1+x^2)^2 within the product rule?
    Exactly
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    (Original post by TenOfThem)
    No attitude here ... We clearly have a different understanding of this thread ... As for your second point ... Are you serious
    Please lose the attitude. If you have nothing useful to contribute to help OP, then please dont at all
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    (Original post by newblood)
    Please lose the attitude. If you have nothing useful to contribute to help OP, then please dont at all
    I am not sure what your issue is


    If you read this thread you will see that my posts have led to the OP understanding how to solve the question

    You posts, on the other hand have simply been aimed at criticising me



    So ...
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    (Original post by TenOfThem)
    Exactly
    Ah so you can't just use chain rule by itself to differentiate it... Thank you
    I was trying to do the "quick chain rule" method
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    (Original post by Peanut247)
    Ah so you can't just use chain rule by itself to differentiate it... Thank you
    That is correct ... Chain rule is used when we have a function of a function

    The 6x was separate to this and needed the product rule
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    (Original post by newblood)
    There is no need for attitude. Please try to be more helpful on the maths forum in future
    (Psst - TenOfThem is one of the more prolific helpers on this thread )
 
 
 
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