### Partial Derivative Functions

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

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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 second derivative of f(x) = (x + 1)^2/(x -1)

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

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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 1) Use the definition of a derivative to find G (x) if G(x) =

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 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

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

Please see the attached file for the full problem description. 1. (a) If f (r, theta) = r^n cosntheta show that (see attached file) (b) If u = y^3 - 3x^2y prove that (see attached file).

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

(a)Find the orthogonal trajectories of the family of curves defined by 2cy + x2 = c2, c>0 State the differential equation of the orthogonal family, and show your steps in obtaining a solution. (b) On the same set of "square" axes, plot at least five members of each of the given family and your family of orthogonal soluti

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 rapidly

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)

Let f be the function whose graph goes through point (3,6) and whose derivative is given by f'(x) = (1+e^(x))/(x^2) a) write the equation of the line tangent to the graph of f at x=3 and use it to approximate f(3.1) b) Use Euler's method, starting at x=3 with a step size of .05 to approximate f(3.1). Use f'' to explain wh

I am taking a course by distance, and my professor provided an example of how to create a Hessian matrix using partial derivatives. He gave another example that just had the solution for us to try on our own. I think that I am somehow not taking the second order partial derivative right. The attached file has the professor