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Math Help - How To Do Differentiation/Derivatives...?

  1. #1
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    How To Do Differentiation/Derivatives...?

    #1 Suppose u and v are functions of x that are differentiable at x=0, and that u(0)=5,
    u'(0)=-3,
    v(0)=-1, and
    v'(0)=2.

    Find the values of the following derivatives at x=0.

    a) (d/(dx))(uv)

    My answer: 13

    b) (d/dx)(u/v)

    My answer: -7

    c) (d/dx)(v/u)

    d) (d/dx)(7v-2u)

    For c and d, I do not know how to read this problem or approach it. I don't know what d stands for or what to do with the numbers surrounding it. Clueless.

    #2 y=(x^2+3)/x

    Find dy/dx by multiplying the factors first, then differentiating.

    My work:

    (I know how to do this be differentiating first, then multiplying the factors, but not the other way around...)

    ((x^2+3)(x) + (x^2+3)(x))/x^2
    (x^3+3x+x^3+3x)/x^2
    (3x^2+3+3x^2+3)/2x
    (6x^2+6)/2x
    6(x^2+1)/2x
    3(x^2+1)/x
    (3x^2+3)/x
    3x + 3/x

    How do you do these...?
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  2. #2
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    Suppose u and v are functions of x that are differentiable at x=0, and that u(0)=5,
    u'(0)=-3,
    v(0)=-1, and
    v'(0)=2.

    Find the values of the following derivatives at x=0.

    a) (d/(dx))(uv)

    My answer: 13 ok

    b) (d/dx)(u/v)

    My answer: -7 ok

    c) (d/dx)(v/u)

    d) (d/dx)(7v-2u)

    For c and d, I do not know how to read this problem or approach it. I don't know what d stands for or what to do with the numbers surrounding it. Clueless. Clueless?, then how did you get the correct solutions for (a) and (b) ? d/dx just means take the derivative w/r to x.

    #2 y=(x^2+3)/x = x + (3/x) ... now take the derivative
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