Calculus

Use a symbolic differentiation utility to find the derivative of the function g(x)=x�ã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeroes of the graph of the derivative.

Please show work, and if you cannot display a graph in your answer, please provide the derivative asked in the first part of the question so I have a foundation to start with. Thanks in advance!

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  1. Sorry, that's x times square root of ((x^2)+1)

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  2. f(x) = x(x^2 + 1)^(1/2)
    f'(x) = (x)(1/2)(x^2+1)^(-1/2)(2x) + (1)(x^2+1)^(1/2)
    f'(x) = (x^2)(x^2+1)^(-1/2) + (x^2+1)^(1/2)

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