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find derivative of f(x)=1/sqx^2+1 by using the definition of derivatives

  • science - ,

    Do you mean
    f(x)= 1/sqrt(x^2+1) = (x^2)+1)^-1/2?

    The derivative would be
    f'(x) = (-1/2)(2x)/(x^2 +1)^(3/2)
    = -x/(x^2 +1)^(3/2)

    The "chain rule" was used.
    df/dx = df/du*du/dx
    with u(x) = u^2 +1 and f(u) = u^-1/2

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