As an application of partial derivative of multi-variable functions, provide one page about Lagrange Multipliers and explain the application of it with an example.

Q: 2. As an application of partial derivative of multi-variable functions, provide one page abou…

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Q: Compute the derivative using derivative rules that have been introduced so far y = (4 - 2x - 3x 2) 5

A: Given: y=4-2x-3x25  ……1

Q: The second derivative test is used to distinguish between maximum and minimum points by determining…

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Q: Use the limit definition of partial derivatives

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Q: What are Partial Derivatives?

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Q: Compute the derivative using derivative rules that have been introduced so far. y = (x 4 + 5)3

A: Given equation is y=x4+53 Applying derivative with respect to x: dydx=dx4+53dx Using the power rule…

Q: Define partial derivative?

A: In multivariable equation, if we want to find partial derivative with respect to any variable then…

Q: 6. A rancher wants to fence off a rectangular corral with an area of 4050 sq. yds next to a river.…

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Q: Use a linear approximation to estimate V65.

A: 653

Q: How is derivatives utilized in solving for the dimensions and total area of a box?

A: Here we to write how is derivatives utilized in solving for the dimensions and total area of a box.

Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: Use the limit definition of the partial derivative to verify the formulas

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the orthogonal trajectories of the family of curves.

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Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

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Q: Find the derivative of the function. y = x 5 Vx3+7 O y'=- 2VX3+7 3x7 5x3 Vx3 +7 3x6 O y'=. 5x4 Vx3…

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Q: What are the maximum and minimum values in application of derivatives?

A: We have to define the maximum and minimum values in application of derivatives.

Q: Find the relative maxima and minima of y by the second derivative test:    y = 2x / 1-2x

A: Given- y=2x1-2x To find- The relative maxima and minima of y by the second derivative test: Concept…

Q: 1. у %3D 4x? — Зх — 2.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: How would you find the stationary points of partial derivative equations coming from a multivariate…

A: Stationary points:

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: can explain for me what is Applications of Partial Derivative ?

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Q: By using quotient rule, differentiate f(x) = (2x* – 7x² + 3x)(x² + 1)-1. Hence, find the gradient of…

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Q: Analyze the stationary points of f(x) = x2ex by applying the second-order derivative test.

A: Stationary points are occurred where the first derivative of the function becomes zero. If the Value…

Q: How can the derivative function definition be applied to this problem?

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Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

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Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

Q: 1. у %3D 4x2 — 3х — 2.

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Q: Find both first partial derivatives. az

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Q: Estimate the derivative of the function f (x) = -3 at the point a = 3. %3D

A: Here given as fx=x3-3 Differentiate with respect to x f'x=ddxx3-3=ddxx3-ddx3=13

Q: Find the slope of the tangent line to the graph of x4 + 5xy - 12x + 11 = dt at the point (1 , 0) on…

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Q: Give information on this application of derivatives:  Optimization

A: Topic:- application of derivatives

Q: Choose the derivative of sec-(æ). 1 1+ 22 1 - 1 1 V1-3 1 aVa - 1 1 1+ 22 1 1 - a2

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Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Find the partial derivative. or (revary) =

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Q: How do you find the partial derivative of a given function using the definition formula?

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Q: Explain how to determine Partial derivatives for x-value ?

A: Partial derivatives :- Let z=fx,y be function of two independent variables x and y. If we keep y  as…

Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.) y=…

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Q: Find the partial derivative for this

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: fox)= x+ ?

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Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: Find the derivative. (Hint: do chain rule. ) * 12° dt 6x 8x6 12x/2

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Q: Solve using partial differentiation

A: Given that  uxy=4eycos2x given that y = 0, ∂u∂y=cosx and u=y2…

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2

Q: What is the definition of the derivative (Difference Quotient)?

A: 2. What is the definition of the derivative(difference quotient)? ans. In single-variable calculus,…