### 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

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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

Find the derivative of each expression, using the product rule, quotient rule, or chain rule. 1. P= e^(2x)/x 2. B= square root of sin * square root of x 3. Find dy/dx using implicit differentiation. (3xy + 1)^5 = x^2

Please see the attached file for full problem description. (a) By making the substitution y = z/x^4, or otherwise, reduce the equation dy/dx +4y/x =sinx/x2 to an equation in which the variables are separable. Solve the equation if y = 0 when x = pi/2 (b) In a circuit di/dt=K(E-Ri) and i=0 when t=0. Find i in

(A) Find and simplify the difference quotient for G(X)=1/x^2. HINT: After finding the difference quotient, simplify by using an LCD to combine the fractions. (B) Using the answer above, find the value of the difference quotient at x=1 with an h=.1 C) Sketch a graph of G(x). Mark the point(1,G(1)) on the graph. Sketch a

I have a first derivative and a second derivative, how do you get from the first to the second, I can't solve it. Please see the attached file for the fully formatted problems. M'(t) = pe^t/(1 - t^tq)^2 M''(t) = pe^t(1 + qe^t)/(1 - (e^t)q)^3

Please see attachment. Please help me solve problem in its entirety. I'm having trouble, most of all, solving the D.E. Thanks. :)

Suppose that the temperature at the point (x, y, z) in space (in degrees Celsius) is given by the formula: W= 100 - x^2 - y^2 - z^2. The units in space are meters. (a) Find the rate of change of temperature at the point P(3, -4, 5) in the direction of the vector v=3i - 4j + 12k. (b) In what direction does W increase most rapi

Find the directional derivative of f at P in the direction of v; that is find D_u f(P), where u=v/{v}: f(x, y, z)= ln(1 + x^2 +y^2 - z^2) ; P(1, -1, 1), v=2i - 2j -3k

Write chain rule formulas giving the partial derivative of the dependent variable p with respect to each independent variable: p=f(x, y, z); x=x(u, v), y=y(u, v), z=z(u, v)