Derivative of function?

F(x)= square root(x) + 7 / square root (x) - 7

Find Fprime(x)

3 Answers

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  • Anonymous
    1 decade ago
    Favorite Answer

    F'(x)=(1/2 )x^{-1/2} -(7/2) x^{-3/2}

    Source(s): h
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  • Guru
    Lv 6
    1 decade ago

    here it is

    F'(x) = (1/2)x^(-1/2) - (7/2)*x^(-3/2)

    Take each term separately.

    square root of x can be written as x^(1/2)

    So, its derivative is (1/2) x^(1/2-1) = (1/2)x^(-1/2)

    Do this for the second term also.

    The third term, '7' is just a constant, so its derivative is just zero.

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  • 1 decade ago

    you can find the value by u/v formula I think you mean

    (sqrt(x) +7)/(sqrt(x)-7)) else it too trivial

    d(u/v)/dx = (udv/dx - vdu/dx)/v^2

    u = x^(1/2)+7

    du/dx = (1/2) x^(-1/2)

    and v = x^(1/2) - 7

    dv/dx = (1/2) x^(-1/2)

    so numerator = (x^(1/2)+7) (1/2)x^(-1/2) + (x^(-1/2)-7) (1/2)x^(-1/2)

    = x^(1/2)x^(-1/2) = 1

    denominator = (x^(1/2) - 7)

    so f'(x) = 1/(x^(1/2)-7)^2

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