23. Let f(x, y) = xy² and let x(s, t) = t² ln(s) and y(s, t) = = s-t Compute of woivos Əs (s, t)=(2,1)

Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: (B) If f(x,t) = fakt e-y²dy, then prove that kfx = ft.

A: (.)  Leibniz rule :  Given

Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

A: Given query is to find the derivative of the expression.

Q: Let F(x, y, z) = x3³yz² - 6x²yz + 9xz - 2y³z. Find F Fxyz' 3x²yz² - 12xyz +9z+ x³z² − 6x²z − 6y²z +…

A: This question is based on Partial Derivative.

Q: If f(r, v) = ry – ry", find 7 + ±),-.y-a

A: The power rule of differentiation states that d dxxp=pxp-1, where p is any real number. Use the…

Q: Suppose f(x, y, z)=x+y+z, h(x,y) = (x + y, x³, y) and g(x) = (x,x²). Calculate d =z=of oho g(x). dx

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Q: Find D and e^(tA) = P e^(tD) P^(-1).

A: Step 1:Find Eigenvalues and Eigenvectors: First, find the eigenvalues (λ) and eigenvectors (v) of…

Q: u = Vx + 5 (x + 1) then du/dx is Зх — 11 Зх + 11 2 Vx + 5 2 Vx + 5 A 3x + 10 Зх — 10 2 Vx + 5 2 Vx +…

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Q: Let r(t) =ti +t³j +tk The normal component of acceleration is an = 6t/2/V9t4 + 2 а. b. an= 4t/2/V9r*…

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Q: Let F(x, y) =x2+xyz+z , find at the point (1,1,1)

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Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

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Q: If xly then gcd(x,y) = y. إختر واحدا:

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Q: O Find Vf, where f(x, y, z) = = e¯(ax+by+cz) with a, b, c some constants.

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Q: Determine if f(x, y) is continuous at (0,0) where x²y² √x² + y² 0 f(x, y) =. if (x,y) = (0,0) if (x,…

A: To determine whether  is continuous at where

Q: If f(x,y,z) = e* and g(x,y,z) = y – z Then, V (fg) will be;

A: Given fx,y,z=ex, gx,y,z=y-z

Q: . Find, from first principles, f(2, -1) for f(x, y) = 2a?y³ + e2y. ,2,,3

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Q: f(x, y) = xy(3-a-y) OA. (1, В. О в. (0, 1) O C. (0,0) O P. (-3,3)

A: Given function is f(x,y)=xy(3-x-y) At first we differentiate it partially w.r.t. x and y and setting…

Q: 4Ux+Uy=U² , U(x,0)=1/1+x²

A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

Q: f(x, y) = ln(+1), g(x, y, z)= e²+y+²+z²+y³+2, h(w, x, y, z) = (4r+wy)²(z-7w). 14.67=(2,4), =…

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: 26. Evaluate the gradint of f (x,y,₁z) = log (= ² + y² +₂²) at (1₁91)-11

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Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

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Q: Show that A Yk= V' Yk+r

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Q: • The Doman of f(x) = 4 – Vx is 1. (2, 0) 2. [-2,0) 3. [2, 00) 4. [-2,2]

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Q: f(x, y, z) = z°y?lna fazyzz =? IIY -2z2 O A. 12y2z2 В. 2x2 -12yz O C. x2 y24 O D. x4

A: Partial derivatives

Q: Where did F(x, y, z) = Em(1,4,5) come from

A: The steps to follow to write a function in SOP form:    1. Write AND terms for each input…

Q: Find the saddle point/s of the function f(x,y) = x + y² +x²y+4 O a. (E ,-1) & (- 2 -1) O b.(4,0) &…

A: Let's find.

Q: O Determine if f(x, y) is continuous at (0, 0) where x² y ² f(x, y)=√x² + y² 0 if (x, y) = (0,0) if…

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Q: Consider f(z, y) = z² + y³ and g(x) = (x, x², z³). .Then D(g(f(x)) %3D O 1× 3 О Зх1 O 2 x1 О 1x2 O 5…

A: consider f(x,y)=x2+y3 anf g(x)=<x,x2,x3>we have to find the dimension of matrix…

Q: The greatest common factor of the numbers 12xy², 54x²y³, and 72x'y is AxByC. Write the value of A in…

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Q: Let g(x, y) = Vx²y². Find 1. g(1, 2) 2. g(4,1) 3. g(2, у) 4. g(x,2) 5. g(w, z – 1)

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: (a) f(2, 1, 2) (b) f(-3, 2, 1) (c) f(0, 0, 0) (e) f(t, 1², –t) (d) f(a, a, a) (f) f(a +b, a – b, b).…

A: Given: The function f(x,y,z)=xy2z3+3 where f is a function of x, y, and z. To find: f(2,1,2),…