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    Hello,

    Could someone help me with how to get the answers to these questions:

    a) f(x) = 12x / (1+x²)

    b) f(x) = ln(1+x²)


    Thanks for your time and help
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    for a) you'd use the quotient rule, so if your f(x) is of the form u(x)/v(x), the first derivative is of the form f'(x)= ([v(x)*u'(x)]-[u(x)*v'(x)])/v^2(x)

    for b), use the standard result that for a function of the form f(x)=ln g(x), then f'(x)=g'(x)/g(x)

    hope that helps and is clear, please say if you dont understand what ive written
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    (Original post by anon2332)
    Hello,

    Could someone help me with how to get the answers to these questions:

    a) f(x) = 12x / (1+x²)

    b) f(x) = ln(1+x²)


    Thanks for your time and help
    You could use the PRODUCT RULE or the Quotient Rule

    I prefer the Product Rule

    y=uv

    \dfrac{dy}{dx}=u\dfrac{dv}{dx}+v  \dfrac{du}{dx}
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    Thanks. I think I understand it. What did you get as the final answer.
    Cheers
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    how about you say what you got as your answer instead. Is this not a question from a book and so have no answer to compare against?
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    On the first, I prefer to use quotient rule:  u and v are two functions of x such that  y = \dfrac{u}{v}

    Therefore  \dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{v\frac{\mathrm{d}u}{\math  rm{d}x} - u\frac{\mathrm{d}v}{\mathrm{d}x}  }{v^2}

    In your question, do you see how we could use  u = 12x and v = 1+x^2 ?

    On the second, use the fact that, where f(x) is a function of x, such that  y = \ln (f(x))

    Then  \dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{f'(x)}{f(x)} where  f'(x) is the first derivative of f(x).

    In your question, do you see how we can use  f(x) = 1+x^2 ?
 
 
 
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