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

Q: Given f(x, y) = x² – 3x?y – y", find fz(r, y) = fy(x, y) = frz(x, y) = fzy(x, y) =|

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Q: + The Range of y [2x + 1] is Z. %3D TO FO

A: We can use the concept of function In order to solve the given problem.

Q: Evaluate F. dr F(x, y) = 5xi + 8yj C: r(t) = ti + v4 - tj, -2 sts 2

A: Calculate drdt. drdt=ddtti+4-t2j      =1i+124-t20-2tj      =1i+124-t2-2tj      =1i-t4-t2j…

Q: Given f(x, y) = 10/2x° + 8y + 6ry", find fz(x, y) = %3D fy(x, y) = %3D

A: Given,  fx, y =10 2x6+8y+6xy5   We have to find fxx, y   and  fyx, y.

Q: Since fy(x, y) = x², find f(x, y). f(x, y) = + g(y)

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Q: 2 13 y+y+y%3Dx"+4X+12%

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Q: Given f(x, y, z) = 2e(z+y), Find fy(0,},-4).

A: here we have to find partial derivative of a function w.r.t. 'y' and here we also use chain rule.

Q: IF f(x,y) = y³e-5x find fryy at (0,1)

A: We need to find the partial derivative fxyy of f(x, y) = y3e-5x at (0, 1). Let us first find fxyy.…

Q: Given f(x, y) = x° + 2xy³ – 2y", find fz(x, y) = fy(x, y) =

A: Given  f(x, y) = x6 + 2xy3 - 2y5.

Q: For the function f(x,y,z) = In (5x + 4y + 9z), find f,, fy, and f,.

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Q: Suppose z is a function of x and y, and csc Vx2 + yz = 2"esin . Solve for dz and ду

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Q: Evaluate F. dr. F(x, y) = 3xi + 4yj C: r(t) = ti + V4 - t²j, -2 s t s 2

A: we know r(t)=x(t)i^+y(t)j^ hence from given x=t, y=4-t2

Q: For the function f(x,y,z) = In (7x+ 2y +5z), find fy, fy, and f,. fx =口

A: Given,           fx,y,z=ln7x+2y+5z

Q: Given f(x, y) = 3® – 3xy - 2y, find fz(x, y) =| fy(x, y) = %3D

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Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

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Q: Find f, and f, for f(x, y) = 10(9x – 8y+ 12)°. fx(Xx.y) = f,(x.y) D

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

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Q: Given f(x, y) = - 5a4 – 4x²y³ + 6y°, find - fa(x, y) = fy(x, y) = %3D fez(x, y) =

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

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.

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Q: For the function f(x,y,z) = In (6x + 7y + 4z), find fx, fy, and f,.

A: Given: f(x,y,z)=ln(6x+7y+4z)To find the fx, fy, and fzddx (ln x)=1x

Q: For f(x, y) = (x²y – 8y)°, find. a) fa (x, y) b) fy (x, y)

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Q: Evaluate F. dr- F(x, y) = 3xi + 8yj C: r(t) = ti + V4 - t°j, -2 st s2

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Q: If f(x, y) = 8xe2y + 8y Inx, then is given by:

A: The given function is: f(x,y)=8xe2y+8y ln x Now, ∂f∂x=∂∂x8xe2y+8y ln x       =8e2y+8yx

Q: Show that the function f(x, y) = (y + ax)²ev+a satisfies the equation given by %3D a2

A: Please see the explanation below....

Q: Find fx and fy from the equation* f (x, y) = In (V²yi 7- 景 3 2y 2y O Option 1 Option 4 五- ん- 1 fy =…

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Q: Find values of x and y such that both f,(x,y)= 0 and fy (x.y)=D0. f(x.y) =x + xy +y² - 3x+2

A: Given that, the function is fx,y=x2+xy+y2-3x+2. Obtain the value of fxx,y.…

Q: Let f(x,y) = 10x^3y^4+ 21xy^2 Find ?yyy

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Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

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Q: If f(x, y) = (8x2 + 8y³)³, then f_(0,0) %3D %3D A) 0 B) 2 C) 8 D) 1 E) Does not exist

A: Let us consider the two variable function f(x,y) Partial derivative of the function with respect to…

Q: If f(x, y) = ecosy, then find Ꭷ f Ꭷ2 f + Ox2 " dy2

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Q: Given f (x, y) = x cos y - ye*, find fx and fy. Compute Dif (3,-2) and Daf (3,-2) if f(x,y) = 5x3 –…

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Q: F(x,y, z) = 5x² + 2y² + 4xy + xz

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Q: Evaluate F. dr. F(x, y) = 9xi + 2yj C: r(t) = ti + V4 - t'j, -2 sts 2

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Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given

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

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Q: Given f(x, y) = – 5x + 6xy° + 3y, find - fa(z, y) = %3D f,(z, y) = !!

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Q: or f(x, y) a + y? – xy +1 -

A: Consider the given function as fx,y=13x3+12y2-xy+1

Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

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Q: Given f(x, y) = 5æ + 6x?y® – 3y', find fz(x, y) = fy(x, y) = fæz (x, y) = | fzy(x, y) = | %3D

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Q: Find f, and f, for f(x, y) = 11(2x – 6y + 5)*. fx (x.y) =D

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Q: Given f(x, y) = x® + 3xy4 – 2y°, find f-(x, y) = fy(x, y) =

A: If f(x, y) is a function then, fx(x, y)  is differentiation of f with respect to x making y variable…

Q: Then: f(x,y) = e*y 12zy O f xyz' x2 2z³y fxxzxy 12z?y? fxxyy 12z3y? x3y fxxxyz

A: The solution is given below :

Q: For f(x,y) = Inx+y³, find f( e 5,6). f( e 5,6) = [

A: We have to find f( e5 , 6)

Q: Evaluate G(x,y)dy , if Gx.y)=2xy ,x 5cost ,y 5sint ,0stsm/3.

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Q: given f (z) = (z +1)° - 3z' what is the value of u

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Q: Evaluate F. dr. F(x, y) = 5xi + 8yj C: r(t) = ti + v4 - t*j, -2 sts 2

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Q: Given: f (x, y, z) = 2x'yz² + 5x°y*z® - x³y? ,5_3 Required: fzyx , fxzz

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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.