(b) Use the Chain Rule for functions of several variables to find e and dw if 4.x2y3 – 1 + 2y and v = - - 9y. (PLEASE DO NOT SIMPLIFY YOUR W = U = | ANSWER). ANSWER: dw ANSWER: dy

Q: Find all values of x such that dy/ldx = 0 where y is the function stated below. x2 y = -3x + 4)

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Q: +5t, y=s - 5t, z = st² d aw/ot by using the appropriate Chain Rule. d aw/at by converting w to a…

A:

Q: If f(x, y) = x3 + yt, what is the partial derivative of f with respect to x? A 3x2 B 4y3 3x²+ 4y3

A: Given fx,y=x3+y4

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A: Recall the chain rule of differentiation:

Q: Please help

A: Let,

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Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

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Q: Find the linearization L(x, y) of the function f(x, y) = V161 – læ2 – 16y² at (-4, –3). L(x, y) = ||…

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Q: (b) Find the first order partial derivative af and for the function f(x, y) = x/y –x²y+ y²

A:

Q: Q3: Use Chain Rule to differentiate the following functions 1. f(r) = (4x² - 3r + 2) 2 2. y = csc(4…

A:

Q: dw the functions w= -5x²-3y².x= cost, and y=sint, express as a function of t, both by using the…

A: Use chain rule for derivative

Q: Find the relative maxima and minima of y by the second-derivative test: (a) y = -2x2 + 8x = 25…

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Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

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Q: Find the linearization of the function f (x) = x° at æ = 1. L(2) = Using this linearlization, f…

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Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = u3 and u = √x

A: Given: ,and . Find out by using the chain rule.

Q: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

A:

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

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Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

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Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

A:

Q: 1. Find the relative maxima and minima of y by the second-derivative test: (a) y = --2x? + 8x + 25…

A: Consider the provided question, According to you we have to solve the part (b), (c) and (d). (b)

Q: When would you use a partial derivative? When you only need to differentiate half of a function. O…

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Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

A:

Q: Find the linearization of the function f(x): L(z)= ab a --4x-5 va a न 4x+3 at z=-1 sin (a) E

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Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

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A: Consider the linearization formula for g(x) near x = a.

Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: 8. (a) For f(x) = Vx, give the linearization at a = 25. (b) Use your answer from part a to approxi-…

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Q: Use the Chain Rule to solve the indicated partial derivatives. Simplify your answers…

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Q: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of rapid increase.

Q: If f(x, y) = x3 + y4, what is the partial derivative of f with respect to х? .A fx = 4x3 || .B fx =…

A: The objective is  to find the partial derivative with respect to x.

Q: Find all the second-order partial derivatives of the following function. 4x - Зу 2? + 3y

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Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

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Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: (b) If g(x) = [,! 1 dt, find g'(x) 4+t2

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Q: 2. Suppose that z is a function of a and y, and F(x2 - y², xy - 2², yz - 2²) = 0. Calculate and…

A: Solution :

Q: Find the partial derivatives of the function V1r2 + 1s² + 6r² w =

A: Given,  w=1r2+1s2+6t2

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Q: Find the second-order partial derivative. 4) Find fyx when f(x.y) = 8x3y - 7y2+ A) 24x2 C) - 28 +…

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Q: Verify the chain rule y = t³. %3D

A: Given query is to solve the expression using chain rule of derivative.

Q: Find the partial derivative of fy for the function * 3 f (x, y) = (3x² + y²) ³ 3x² (3x² + y²)²…

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Q: d²z d12 given that z = In a) Use chain rule to find dt2 x = est and y = t².

A: Derivative of the function

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

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A: I have appended the formula used in the solution part

Q: Find L(x) (Linearization function), given f(x) = ev2x at the value a = 2.

A:

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 16

A: