Let h(x) = f(g(x)), where f and g are differentiable on theirdomains. If g(1) = 3 and g′(1) = 5, what else do you need toknow to calculate h′(1)?

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: 1. Find the first partial derivative of z with respect to x if x'y+ y°z+ z'x = 11.

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Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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Q: Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the…

A: Consider the given function. fx,y=2xy+y2+2x-1 Find the derivative with respect to x. fx=2y+2 Put the…

Q: Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the…

A: We have, To find the critical point, we have to take the partial derivative of the function, and…

Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Determine the second-order partial derivative for the indicated function f(c,y) = cos(2x² – 3y?)…

A: Partial derivative of a function g(x,y) with respect to x is the derivative of g(x,y) keeping y…

Q: Find the critical points of the function f (x, y) = -x2+ 4xy+ xy2 and determine whether the critical…

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Q: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

Q: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

Q: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

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Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Supose z is implicitly defined by the equation qy+ 3x + xyZ + 32=9 in an enmrament of the point…

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Q: Find the first and second order partial derivatives for z x2 sin (3x + 2y).

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Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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Q: 2. IShow, using the definition of the derivative, that the function f(x, y) differentiable at every…

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Q: If z = f (x, y) is a function that admits second continuous partial derivatives such that image1 A…

A: Given z=fx,y such that ∇fx,y=300−12x2−12y2,18y2−24xy. Here, ∇fx,y=fx,fy=300−12x2−12y2,18y2−24xy.…

Q: Find the Partial derivative of f with respect to y for * 2. y² f (x, y) = x + y

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Q: Let z = z(x, y) be a continuous function of x and y defined implicitly by In(3æ* + 4y* + zyz*) = =…

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Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

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Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: If c is a critical point and the derivative of the continuous function f (x) doesn't change from…

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: 1, t 1 differentiable at t = 1.

A: As per bartleby guidelines we only give first question answers.

Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: Let z = x+iy and f(2)=√√|xy|. Show that ƒ(z) satisfies the Cauchy-Riemann equations at the origin,…

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Q: Find the first and second order partial derivatives for z = x² sin (3x + 2y).

A: As we know that; The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x And The first order…

Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

A: Given f(x,y,z)=cos(cos(x3+z2))+x2ln(y2+z2).We need to find the partial derivative fxxyz for the…

Q: If f(x, y, z) = 2 sin(100xy) In(2), compute the value of the limit f(1, h, e) – f(1,0, e) lim h→0 h

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Q: Compute the indicated partial derivative. g(x, у) %3 сos(x + ) 9xxy

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Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How…

A: We have f(x, y)=x2 + y2 and g(x, y)=x2 - y2 By finding the partial derivatives fx=2x, fy=2y, gx=2x,…

Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

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Q: (or axay дудх Calculate the second-order partial derivative of f(x.v) = xy with respect to x and y,…

A: Given  f(x,y)=xy

Q: Find the critical point of ƒ(x, y) = xy + 2x - ln x2y in the open first quadrant (x >0, y>0)…

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Q: Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your…

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Q: (b) Sketch the graph of a function that has a local maximum at 3 and is continuous but not…

A: To sketch the graph of the function which is local maxima at 3 and not differentiable at 3

Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 5x + 6y < 7. 1. Absolute minimum of f(x, y) is…

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Q: Find the absolute maximum and minimum values of the f(x,y)= x²-2xy+y² function over the D region and…

A: In this question, we have given a function and the region D in figure the function f(x,y) and D are…