f(r, y) = = f(x, y) = ", (2, – 2)

Q: 9. If f(x, y) = x³ + 4xy² + y3 %3D show, that f (ax, ay) = a³f (x,y) %3D

A:

Q: 10 If f(x,y)=xª+6/y- 10 Then fxyx Vy

A: Find the third order partial derivative

Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: Which of the following is the function h(x,y) that satisfies the equation h(x, y).fxx+ X.fxy-fyy =0…

A: We will calculate all the partial derivativea and proceed

Q: Find fx, fy, and fz, and evaluate each at the given point. f(x, y, z) = x2y3 + 2xyz − 6yz,    (−3,…

A: To determine the partial derivatives of given function at point (-3, 1, 3).

Q: if f(x,y)= ln(x^2 +y^2), find fxx(x,y) + fyy(x,y)

A:

Q: Suppose f(x, y, z) =

A: Given,            f(x, y, z)=1x2+y2+z2 and W is the bottom half of a sphere of radius 6.

Q: Find Duf at P. 2 + 2. 5,3 4 f(x, y, z) = 6x³y°z*; P(1, – 2, 1); u = Duf i

A:

Q: Find f, and f, and evaluate each at the given point. 8хy f(x, y) = V3x2 (1, 1) + 6y2 fy(x, y) =…

A: Answer is given below

Q: Find fx (x,y) and  fy (x,y).  Then find fx (2, -1) and fy(-4,3) ƒ(x, y) = 4e3x + 2y

A: fx,y=4e3x+2y

Q: Given f(x,y)= x^6 - 5x^2y^2+2y^4, find fxy(x,y)

A: By using partial differential property

Q: Find fx (x,y) and  fy (x,y).  Then find fx (2, -1) and fy(-4,3)

A: The given function is fx, y=ln1+5x3y2. Obtain the partial derivatives as follows. fxx, y=∂∂x…

Q: If f(u,v,w)=u+v2sinw  and u=x−y, v=y−z, w=z−x find  fx+fy+fz=?

A:

Q: If Z = x.n. f .f (**²), then show that: X. Zx + y.Zy = y

A:

Q: Find fx fy, and f₂, and evaluate each at the given point. f(x, y, z) = x²y³ + 2xyz - 7yz, (-3, 1, 3)…

A:

Q: Given f(x, y, z) = x³yz². Find f.(1,1,1).

A: The equation we have , f(x,y,z) = x3yz2 We have to find out fz, Now we differentiate f(x,y,z) with…

Q: 4,5 f (x,V)= Sx"y%,compute fx and fy

A:

Q: 2: find fx, fy, and f2. a f(x, y, z) = 1 + xy? - 2z? 5 f(x, y, z) = x - Vy2 + z² c) f(x, y, z) = e 2

A: partial derivative

Q: Find ƒxx ( x, y)  and ƒxy( x, y).

A: Given, fx,y=3x+yx-1. The objective is to find fxxx,y and fxyx,y.   fxxx,y is found as follows: First…

Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

A:

Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

A:

Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

A:

Q: Let f(x,y,z) = x2yz4 + 4xy²z+y²z - 3y³z Find fxyz

A:

Q: f(2) — и(х, у) + jo(x, y) и(х, у) — е% сos x — х f (0) = 1

A:

Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

A:

Q: Find fx, fy, and fz, and evaluate each at the given point.…

A: We have to find fx,fy and fz for a given function fx,y,z=x3yz2 and also we have to evalute fx,fy and…

Q: Find fy(x,y) and fy(x,y). Then, find fy(- 3,1) and fy(1, – 4). f(x,y) = In |7 + 4x°y²|

A: Let f(x,y) be the given function .Then fx is the derivative of f with respect to x  , treating y as…

Q: If f(x.y,z)= y + xz then f ,(1,1,1) =

A: The given function is  f(x, y, z) = y5 + xz

Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

A:

Q: 2. Let f(x,y)=xe" and find a) fx, fyr fy

A:

Q: x2 If w = x".f then show that: + y², X. Wx + y. wy = nw.

A:

Q: Vy + z f(x, у, 2) 3 (а) f(1, 5, 4) (b) f(6, 7, –2)

A:

Q: 3 4 If f(x, y) = x3 + 5x?y + y3 and u = calculate Du?f(3, 1). 5' 5

A:

Q: 1. Given f(x, y) = 4x³y², evaluate f;(1, y) and fy(x, 2).

A: We know that partial derivative of f with respect to x is denoted by fx  and partial derivative of f…

Q: 9. Find fx and fy and f; for f(x,y,z) = (x² + y² + z²)~1/2 %3D

A:

Q: Find fy and f, for f(x, y) = 10(4x – 5y + 11)°. f, (x.y) =O fy(x.y) =|

A:

Q: The values of fx , f y and f, at (1,1,1) for the function f (x,y,z) = x² + xyz +z are fy= Choose. +…

A:

Q: _et f(x, y) = xe - x². Calculate fx (x, y) and Jy (x, y).

A: To find the partial derivative.

Q: If f(x,y)=x2+2y2, then fx(2,1) and fy(2,1) are...

A: f(x,y)=x2+2y2,find fx(2,1) and fy(2,1)

Q: 9. Given f(x, y) = x?y – 3y*. Find fx, fxx, fy and fyy

A:

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

A:

Q: Find fx and fy, and evaluate each at the given point f(x, y) = exy2,   (ln 3, 2)

A: Given:  f(x, y)=ex y2 ;    (ln 3,  2)To…

Q: f(x,y) = e*y Then: 2z3y fxxy x2 2z3y fxxz = x2 2z y O fwy= x2 2z³y2 fx

A: None of the options are true.

Q: Let f(x,y,z)=x^3 yz^2+4xy^2 z+y^2 z-2y^4 z^3 find fxyz

A: Use the following formulae, to obtain the solution.…

Q: 5. Find fx, fy, and fz given x®y? f(x, у, 2) z4 %3D

A:

Q: Find the highest point, low point and saddle point (if any) of the f(x, y, z)=3x² + 2xy + y²

A:

Q: [f(x)dx, if f(x) = Vx -k+1;k-13x <k,k = 1, 2,..

A:

Q: Given the function: f(x, y, z) = x²yz + xy+ +1 find: fz(1, 2, 3)

A: We will find fx1,2,3 in the following step.