### Derivatives

A) f(x) = -4x-1 (-4x to the -1) f'(x) =

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A) f(x) = -4x-1 (-4x to the -1) f'(x) =

Please see attached file for the six fully-formatted questions with calculus involving limits and differentiation.

Compute the first-order partial derivative of the given function z=xy^2/x^2y^3+1

Please show or explain step by step process. Please use proper notation. Volume: Find the volume of the solid generated by revolving the region bounded by the graph y=xe^(-x), y=0 and x=0 about the x-axis.

The product rule for radicals is ... (see attached) Solve ... (see attached)

The Problem is attached

See attachment

How do you find the derivatives of: ln(1 + 5/x) and of: (ln(1 + x)/x) / (1/x) ?

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

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

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) =

1) Differentate the equations a) y=8/5xsquared b) y=4cosX - 3ex 2)The fomula 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 dC

I have done most of the calculations but require confirmation.

Show that the 2-cycle of the quadratic map is stable if 3/4<5/4. The quadratic map is x(n+1)=x(n)^2-c.

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

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!

If f(x,-y) = x^3 + cosy, determine fxx and fxy.

Please see the attached file for the fully formatted problem. Find G'(x) if G(x) = f1 x xt dt

Find the derivative: y = (x^2 - x +1)^-7

1) Find the derivative if y = (x^4 + 2x)(x^3 + 2x^2 +1)

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

See attached

See attached file for full problem description.

Questions are in the attached file. For #1, find and sketch the domain of the function For #2, find the indicated partial derivatives

Differentiate the following.... x^2-4xy+3ysinx=17.

Solve by double integration in polar coordinates: Find the volume bounded by the paraboloids z = x^2 + y^2 and z = 4 - 3x^2 - 3y^2

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

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:

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.

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