I. If f(x, y) = x² – y² + 4xy – 7x + 10, find (a) f(2, 1) (c) f(x + h, y) (b) f(-3, 5) (d) f(x, y + k)

Q: Find fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: -16 1Δίνεται η συνάρτηση f)- 2x+8x i) Ποιο είναι το πεδίο ορισμού της f i) Να απλοποιήσετε τον τύπο…

A:

Q: 3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

A: We know, ddxxn=nx(n-1)  , for any real number n. ddxln(x)=1x

Q: If f(x,y,z)=x²y³-y²z³ Then f;= -3y²z2 Jlgn

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Q: then fxy Q4: If f (x, y,z) = x²y³ – y²z3 %3D -

A: we have to find partial derivative

Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

A:

Q: a) f„(x, y) b) f (х, у) уу ух 1 3 Зу'х + 5ху 3y'x .3. f (x, у) 16x*y4 -

A: (a)

Q: 2 X+y +Z=lo Gouss eleminahin 3 X+ 2Y4 32=18 X +uy+ 9Z= 16 ماركة العرض من قبال

A:

Q: 4 + 8z is The antiderivative of the function f(x) -4 4.0z +c 4. + 4.0z2 + c 4 | 4.0z? + c 8 + 2.0r2…

A: Using anti derivatives means integration.

Q: 12. f(x, y) = x' – 2x – y + 4y, P = (1, 2). -

A:

Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: If f(x,y)=xe"*/2+135x?y3, then əx²əy³ at (1,1) is equal to

A:

Q: Find y' by implicit dif ferentiation for 2y³+4x² –y = x6 . 6x5- 8x y '=- 6y2 – 1 A 6r5 + 8x B 6y2– 1…

A: Given, 2y3+4x2-y =x6 We have to find y' by using the implicit differentiation.

Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

A:

Q: If f(x,y.z)= In(x2 +y³ +2z5), Find and dx² dz2

A:

Q: 4) f(x, y,z) = /1– x² – y² – z²

A: Domain is the subset of R3 where the function is defined

Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: 4. Sketch: (a) f(x, y) = 4 – x² – y? f (x, y) = x² – y² + 2x ** (b) (c) f(x, y) = /A– x² – 4y² f (x,…

A: 4. (a) We are to sketch the graph of the function f(x,y)=4-x2-y2 \

Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: Зх — 4у + 23 (a) f(x, y, z) = '9 – x² – y² –. - V2t – 4 x² – y? - (b) g(x, y, t) : -

A:

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

A:

Q: (b) Differentiate (Vx+ 1) with respect to x. 2/3

A: as per our guideline we can solve maximum one question you can repost other questions

Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

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Q: x, prove that y¨= 2(y² +1)(3y² +1).

A:

Q: xyz 9. f(x, y, z) = x² + y2 + z2

A: Givenf(x,y,z)=xyzx2+y2+z2To find Domain of above functions

Q: Q3: if f(x)= xy+2x-5y =2 then dy/dx3D a- b- C-

A: We know that dy/dx mean difernciate f(x) with x. From this we will get our answer.

Q: Find fr, fu, and f.. -0.5 f(x, y, z) = (4x² + 6y² + 3z²) fz = fy = f: =

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Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

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Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: Then: f(x, y) = exy 2z3y fxxy 2 2z?y fxxz' XXZ 2z y Ofxyy= x2 Of- 2z3y2 fx² X

A:

Q: The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C…

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: 2. Verify the following derivatives : d а) dx 45x +(Vx + b) 4Vx(ax² + bx +c)]=,_ d 1 -(5ax² + 3bx +…

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Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: 9 2. If fS(x)dx= 37 and g(x)dx=16, = 16, find [2f(x)+3g(x) ]dx- %3D 0.

A:

Q: 7x + 19y fe is: dy If f(x, y) then 7а — 19у - 266x (7x 19y)2 - 266x (7x + 19y)² 266x (7x – 19y)² -…

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Q: Q3: 1f f (x,y) = 6x*y5 + 4x*y4 Prove that: f (x,y) * fxxyy fxx * fyy = 1

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Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

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Q: 190.19 b.) 6Xi t 15X2-24 y3 f 40x4 > 69.8 ¥3 15X, + 9x2 -13 V3 -24Y1 参3X t18 y3- 1 Xy = -163 " xy=…

A: Here we use a = x1 b = x2 c = x3 d = x4

Q: note that X - y +z = e2 and 4x – 3y + 2z = e2

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Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 11-20.

A: (10)Consider the provided function, fx,y=x2+2xy Find all the local maxima, local minima, and saddle…

Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

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Q: f(x,y) = 3y3 – 2xy + 12y – 3x² – 8x – 16 then fy equals ух

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Q: = 0 for F = yz²î +xyj + yzk

A:

Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

A:

Q: (b) f(z)= (4 – 5e*)³ x² + 1 (c) f(r)= ez %3D (d) f(z) = e=²–5z+4 ez-5x+4 (e) f(x)=xe² – e² = re² –…

A: We can solve this as follows: