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    Its asking me to differentiate the function f(x) = 1/(x^2 + a^2)

    am I right in thinking that I need to change it to partial fractions form?
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    (Original post by fuzzybear)
    Its asking me to differentiate the function f(x) = 1/(x^2 + a^2)

    am I right in thinking that I need to change it to partial fractions form?
    Just use the quotient rule. Is a a constant?
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    (Original post by keromedic)
    Just use the quotient rule. Is a a constant?
    yeah 'a' is a constant
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    (Original post by keromedic)
    Just use the quotient rule. Is a a constant?
    I don't understand though, I thought the quotient rule can only be used when you have a function on the top and bottom of a fraction

    in my question there, the top part of the fraction is just '1', there are no 'x's' on the top
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    Here you go.

    http://i.imgur.com/pCRGCoi.jpg
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    f(x) = 1/x^2 + 4^2 (where a = 4)

    f(x) = (x^2 + 4^2) ^ -1

    dy/dx = -2x(x^2 + 4^2)^-2

    Move the denominator to the numerator and use the chain rule.

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    (Original post by fuzzybear)
    I don't understand though, I thought the quotient rule can only be used when you have a function on the top and bottom of a fraction

    in my question there, the top part of the fraction is just '1', there are no 'x's' on the top
    You do have a function on top, y=1 is still a function. You don't need the quotient rule though (but it would work), the chain rule is enough.
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    (Original post by fuzzybear)
    I don't understand though, I thought the quotient rule can only be used when you have a function on the top and bottom of a fraction

    in my question there, the top part of the fraction is just '1', there are no 'x's' on the top
    The '1' can be considered a function, it's just a constant function, so d(1)/dx = 0. You can also do what the HazimQ did (chain rule).
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    (Original post by HazimQ)
    f(x) = 1/x^2 + 4^2 (where a = 4)

    f(x) = (x^2 + 4^2) ^ -1

    dy/dx = -2x(x^2 + 4^2)^-2

    Move the denominator to the numerator and use the chain rule.

    Your first line is very ambiguous. Use brackets or Latex
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    (Original post by fuzzybear)
    I don't understand though, I thought the quotient rule can only be used when you have a function on the top and bottom of a fraction

    in my question there, the top part of the fraction is just '1', there are no 'x's' on the top
    A function can be constant, i.e independent of x. The quotient rule still applies
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    I applied the quotient rule and got:

    -2x / (x^2 + a^2)^2

    -2x / x^4 + 2*(a^2)*(x^2) + a^4

    is that correct?
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    (Original post by fuzzybear)
    I applied the quotient rule and got:

    -2x / (x^2 + a^2)^2

    -2x / x^4 + 2*(a^2)*(x^2) + a^4

    is that correct?
    Indeedy. Expanding the bracket makes it ugly, but either way its right. :2euk48l:
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    (Original post by Phichi)
    Indeedy. Expanding the bracket makes it ugly, but either way its right. :2euk48l:
    sweet, cheers mate
 
 
 
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