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    Calculus - Derivatives and Numerical Values

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    Need help with calculus homework problems.

    In Exercises 41-48, find dy/dx

    44. 5x 4/5 + 10y 6/5 = 15
    ____________________________________________________________________

    54. a. By differentiating x 2 - y2 =1 implicitly, show that dy/dx = x/y

    b. Then show that d2y/dx2 = - 1/y3.

    _____________________________________________________________________

    Numerical Values of Derivatives
    56. Suppose that the function f(x) and its first derivative have the following values at
    x = 0 and x = 1

    x f(x) f'(x)
    0 9 -2
    1 -3 1/5

    Find the first derivatives of the following combinations at the given value of x
    a. f(x), x = 1
    b. , x = 0
    c. f , x =1
    d. f(1 - 5 tan x), x = 0

    e. f(x) , x = 0
    2+cosx

    f. 10sin f2(x), x = 1

    62. If x1/3 + y1/3 = 4, find d2y/dx2 at the point (8,8)

    68. For what value or values of the constant m, if any is

    f(x) =

    a. continuous at x = 0?

    b. differentiable at x = 0?

    Give reasons for your answers

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    https://brainmass.com/math/calculus-and-analysis/calculus-derivatives-numerical-values-237165

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    The solution file is attached.

    In Exercises 41-48, find dy/dx
    44. 5x 4/5 + 10y 6/5 = 15
    5(4/5) x^(-1/5) + 10(6/5) y^(1/5) (dy/dx) = 0
    4 x^(-1/5) + 12 y^(1/5) (dy/dx) = 0
    dy/dx = -4 x^(-1/5) / 12 y^(1/5) = -1/[3 (xy)^(1/5)]

    54. a. By differentiating x 2 - y2 =1 implicitly, show that dy/dx = x/y
    b. Then show that d2y/dx2 = - 1/y3.
    (a) 2x - 2y(dy/dx) = 0
    dy/dx = 2x/2y = x/y
    (b) d^2y/dx^2 = [y - x(dy/dx)]/y^2
    = [y - x(x/y)]/y^2
    = [y^2 - x^2]/y^3
    = -1/(y^3)

    Numerical Values of Derivatives
    56. Suppose that the function f(x) and its first derivative have the following values at
    x = 0 and x = ...

    Solution Summary

    The derivatives and numerical values in calculus are determined. Complete, Neat and Step-by-step Solutions are provided in the attached file.

    $2.49

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