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    Derivatives

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    Derivatives

    Solve the following two equations. In each case, determine dy/dx: a.)y=xcos(2x^2) Is this right? y'=x(-sin)(2x^2)(4x) =-4x^2sin(2x^2) b.)y=xe^-x^2 Is this right? y'=-xe^-x^2+1(e^-x) =-xe^-x^2+e^-x

    Derivative Approximation Exact Value Function

    Approximate the derivative of y=x^3 at x=2 by assuming delta x = 0.001 and determining the corresponding change delta y. Compare the approximate value with the exact value. This is what I did - does it look at all right? y(2)=(2)^3=8 y(2.01)=(2.01)^3=8.120601 delta y=8.120601-8=0.120601 dy/dx~delta y/delta x = 0.1206

    4724

    Category: Business > Management Subject: Management Science Details: 1. Which of the following statements are true for f(x) = x2? (Chapter 10) a. f(x) is a concave function b. f(x) </= 20 is a convex set c. f(x) >/= 5 is a convex set d. none of the above 2. Which of the following statements are true for f(x) =

    Differentiation and Rate of Change Word Problems

    1) Differentiate the equations a) y=8/5xsquared b) y=4cosX - 3ex 2)The formula C=60=t3/12 This equation refers to a machine in a workshop. This machine costs £C to lease each week according to the formula and t is the number of hours per week worked by the machine. The rate of increase of cost during the week is given by

    Product Rule and Chain Rule Calculations

    I have done most of the calculations but require confirmation. a) Use the product rule to show that if m is a positive integer then, b) By applying the product rule and the chain rule of differentiation to the functions and derive the quotient rule. That is, show that Assume that for any

    Differentiation : Critical Point - Find Maximum Value

    A manufacturer produces cardboard boxes that are open at the top and sealed at the base. The base is rectangular and its length is double its width. Let x denote the width in metres. the surface area of each such box is fixed to be 3 square metres. The manufacturer wishes to determine the height h and the base width x, in metres

    Directional Derivative

    Find the directional derivative of f(x,y) = 2x^3-y^2+xy at the point (1,2) in the direction of the vector (1,3). Be careful: That direction vector isn't a unit vector!

    Chain Rule

    Please see attached file for problem. thanks

    Derivative Functions Computed

    Please see the attached file for the fully formatted problems. Find the derivative (y) if y = 3x^4 - 2x^3 - 5x^2 + xpi + pi^2

    Multivariable Calculus : Triple Integral - Cylidrical Coordinates

    Solve by triple integration in cylindrical coordinates. Assume that each solid has unit density unless another density function is specified: Find the volume of the region bounded above by the spherical surface x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 + y^2

    Multivariable Calculus : Integral

    Evaluate the integral of the given function f(x, y) over the plane region R that is described: f(x, y) = x ; R is bounded by the parabolas y = x^2 and y = 8 - x^2

    Using Dynamic Programming to Solve Problems

    Please see the attached file for the fully formatted problem. Use Dynamic Programming to solve: 1. Min f(x-bar) = 3x21 + x22 + 2x23 s.t. Sx1 + 2x2 +x3 >= 18 DP Formulation:.... Min s.t. Stage 1: Stage 2: Stage 3:

    Implicit Differentiation Function

    An function y=f(x) is defined implicitly by the formula x=tan(y), with the condition y epsilon (-pi/2, pi/2). Find and formula for its derivative, then obtain the formula for f'(x) in term of x alone.

    Derivatives of SOHCAHTOA

    Calculate y' (y prime) 1. y = cos(tanx) 2. y = e^(-1)*(t^2-2t+2) 3. y = sin^(-1)*(e^x) 4. y = x^r*e^(sx) 5. y = 1/(sin(x-sinx)) 6. y = ln(csc5x) 7. x^2 cosy + sin2y = xy 8. y = ln(x^2*e^2) 9. y = sec(1+x^2) 10. y = (cosx)^x