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!

  1. 👍 0
  2. 👎 0
  3. 👁 608
  1. Sorry, that's x times square root of ((x^2)+1)

    1. 👍 0
    2. 👎 0
  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)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    y = (ln x)^(cos4x) Use logarithmic differentiation to find the derivative of the function.

    asked by John on October 11, 2011
  2. Economics

    Why do people routinely stuff themselves at all-you-can-eat buffets? Explain in terms of both utility and demand theories. At any level, the marginal cost of take another bite at an all-you-can-eat place is zero. In terms of

    asked by Kayla on February 4, 2007
  3. Calculus 1

    Use logarithmic differentiation to find the derivative of the function. y =sqrt(x)^3x

    asked by TayB on March 12, 2015
  4. MATH

    Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. f(θ) = 8 sin(θ) − θ, (0, 0)

    asked by Anonymous on February 13, 2012
  5. economics

    The owner-manager of Good Guys Enterprises obtains utility from income (profit) and from having the firms behave in a socially conscious manner, such as making charitable contributions or civic expenditures. Can you set up the

    asked by Ashaki on May 11, 2012
  1. Math

    A cable 16 m long runs from the top of a utility pole to a point on the ground 4 m from the base of the pole how tall is the utility pole to the nearest tenth A. 15.5 m** B. 16.5 m C. 256 m D. 16 m

    asked by Anonymous on February 7, 2019
  2. Economics - Marginal Utility

    If the price of a cheeseburger is $2 and the price of a bag of french fries is $1, and you have $7 to spend (and you can spend all of it). What is the utility-maximizing combination of cheeseburgers and french fries? Wouldn't that

    asked by Tracci on April 1, 2007
  3. Economics

    2.The owner-manager of Good Guys Enterprises obtains utility from income(profit) and from having the firm behave in a socially conscious manner, such as making charitable contributions or civic expenditures. Can you set up the

    asked by Jorie on May 5, 2010
  4. pre-cal: graphs of functions- fill in the blank

    To find the domain of a function from its graph... To find the range of a function from its graph... To approximate the relative minimum or maximum of a function using a graphing utility,... Let a(,f(a)) and (b,f(b)) be two points

    asked by Anonymous on September 16, 2007
  5. math

    Find the derivative of the function f by using the rules of differentiation. f(x) = x^4 - 4x^2 + 3 f '(x) =??

    asked by Ashton on March 1, 2013
  6. Economic

    1. The principle that states that the more you have of something, the less satisfaction you will get from an additional unit is the a. law of demand. c. law of equilibrium. b. law of diminishing marginal utility. d. price

    asked by Candace on March 31, 2010

You can view more similar questions or ask a new question.