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Derivatives

Partial Derivative Functions

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

Derivative Functions Solved

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

Differentiation : Second Derivatives

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

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Derivatives using the Chain Rule

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

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Derivative

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

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

Use the Definition of a Derivative

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

Partial derivative of one function in relation of a vector

See attached file for full problem description.

Domain of a Function and Partial Derivatives

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

This problem demonstrates the technique of implicit differentiation.

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

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 : Double Integral - THe Polar Coordinates

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

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

Derivatives using product rule, quotient rule, or chain rule.

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

Polar Coordinates : Solving Derivatives and Circuit Problem

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

First Principle in Evaluating Derivatives

(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

Partial Derivatives Problems

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).

Going from First to Second Derivative

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

Working with orthogonal trajectories

(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

Rate of Change of Temperature at a Given Point

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

Directional derivative functions

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

Chain Rule Partial Derivative

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)

Derivative of a function problem

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

Partial derivative question

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