13. Use the chain rule, in Leibniz notation, to find dx dy at the given value of x. а. у %3D Зи? — 5и + 2, и %3D х? — 1,х %3D 2 b. y = 2u + 3u², u = x + x,x = 1 c. y = u(u² + 3)³, u = (x + 3)², x = -2 %3D %3D

Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and 0,

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Q: Transform the following Bernoulli differential equation of the form 2+ P(x) · y = dx Q(x)y" or +…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1. (a) Find dy/dx for y = 1 + (x² – 1)(x³ – x) without first expanding the bracket. | 1+ u (b) Find…

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Q: dw Use an appropriate form of the chain rule to find dt w = In(10x² – 4y + 5z³); c = t', y = tỉ, z =…

A: From the given function: w=ln10x2-4y+5z3 ; x=t12 ; y=t23 ; z=t-2 As we know that: The Power law:…

Q: Consider the ODE y' = y(1 – 4) • What is the order of the D.E.? Is it a linear or a non linear D.E.?…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (3y) at the points (0,0) and0,

A: Answer is given below

Q: Q1. Use the Laplace Transformation to solve the following linear differential equation system. yi -…

A: Apply Laplace transform to the given set of equations.

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

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Q: -2+z) ds over t e point (0, 0, 0)

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Q: Identify the following differential equations according to its type/classification. Give the (a)…

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Q: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

Q: Əz Q3.If Z= f(x,y) = 4 e In(y), and x = ln (u cosv), y = u sinv, use chain rule to find : E * ди Q4.…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Here we find the first order differential equation of given function.

Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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Q: Find the differential equation defined by the transfer function : 2+2s+1 g3+252+4s+2 O d'e + 2 + 4…

A: We will find out the required differential equation.

Q: 30 -20 -10 Compare dy with (r-y} dydx 10 20 30

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Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: EXAMPLE 1 Differentiate y = In(x³ + 9). SOLUTION To use the Chain Rule, we let u = x + 9. Then y =…

A: Explanation is given below..

Q: Find the differential dy: y = In(sec² ( 3"-2*+5)). Find the differential dy: y = In(sec? ( 3-2x+5…

A: We have to differentiate given function

Q: What is the differential equation obtained by eliminating the parameter A from the relation y =A +…

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Q: O Classify the partial differential equation which represents parabolic or hyperbolic or elliptic:…

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Q: Suppose z = x² sin y, x = 2s2 + 3t2, y = 4st. dz and A. Use the chain rule to find ds as functions…

A: Given: z=x2siny x=2s2+3t2 y=4st To find: Using chain rule, ∂z∂s and ∂z∂t ∂z∂s1,-2 and ∂z∂t1,-2

Q: Suppose w = In(8x² + 2y² + 3z²), ¤= 9 cos(t) , y = 9 sin(t) , and z = 8Vt. Compute dw/dt in two…

A: The partial derivative of a multivariable function with respect to any of the variables can be…

Q: () 2. If k = w3 – wv², w=xy, v = w+ x, find and using: dw a) the chain rule b) differentials.

A: Given: k=w3-wv2, w=xy, v=w+x   To find: (∂k∂w)x . (∂k∂x)w  using chain rule and differentials

Q: 1) Create a in solving ODE 3 of the for m: flow chart / road map y" + t p(a) y' (2) = 0 .

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Q: dw Use an appropriate form of the chain rule to find dt In(14.x² – 4y + 523); x = ti, y= tổ, z = t-2…

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Q: Select the differential equation that matches the given slope field. ||| 5| / | 44 / | / 34 || / 2t…

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Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A+…

A: In this question we need to find a derivative of the given equation.

Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

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Q: Determine the differential equation of the family of lines passing through (h, k). A. (y- k) dx -…

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Q: Let y = 5√√. Find the change in y, Ay when x = 2 and Ax = 0.1 Find the differential dy when x = 2…

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Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ ( 1. (D³ - 5D² + 3D + 9)y = 0 2. (D³ - D² –…

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Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: 5. Test the ff ODE for exactness and find the general solution of the DE (2x + 3y) dx + (3x + 4y)…

A: To solve Differential equation.

Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

A:

Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: ди and ди ди Q3. If u = e"" sin p, p= sin x, q = z' In y, r=1/z, use chain rule to find

A: Find your answer below

Q: 19. Let f(x, y, z) = + sin(3z) + e"-2". Find the rate at which f is changing at (2, 4,0) in the…

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Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: dz a²z and 1 a) Find- Usin chain rule. If z = e*y – Sin xy, x=-, y=t? дх ду dt

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Q: 1. How many stable equilibria does the following autonomous differential e y' = y³ + 4y² + 4y

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Q: Find a linear differential operator that annihilate the given function a) y=7e2x b) y=x+3xe6x

A: We know that gD is annihilator of y if gDy=0 (a) y=7e2x Differentiating wrt x, Dy=7×2e2x, D=ddx is…

Q: Consider the following simultaneous equations model. Assume that x is exogenous. yi = Bx + e Y2 =…

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Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Differentiating the given relation y with respect to x , we will eliminate A .

Q: 1-t2 The differential of u=In, is 1+t?

A: Given u=ln1-t21+t2

Q: If (х, у) %3D х" у"is an integratingfactor of the the DE. (1+ 3ху)dx + (ху-1 +x?)dy %3 0 Then, the…

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Q: Q1) Suppose w =÷+ ?, x = cos² t, y = sin² t, z = ; Evaluate dw at t = 3, by using the Chain Rule dt

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.