In Exercises 71–74, find a function z = f(x,y) whose partial deriva- tives are as given, or explain why this is impossible. af Зx?у? — 2х, дх af = 2xy + 6y ду 71. af af = 2xe* + x?y?e** + 3, дх 2r*ye»* – e" ду 72. af 73. дх 2y af 2x (x + y)²' ðy (x + y)² af af = x cos (xy) ду 74. — ху сos (ху) + sin (ху), дх

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Q: Use the Chain Rule to evaluate the partial derivative ah at the point (q, r) = (1,2), where h(u, v)…

A: ∂h∂q=(∂h∂u×∂u∂q)+(∂h∂v×∂v∂q)∂h∂q=ev×4q3+uev×r2Substitute q=1 , r=2⇒u=q4=(1)4=1and v=qr2=1×(2)2=4

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A: given,          any function fx,y at a,b

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A: The partial derivative of any function can be calculated by partially differentiating it with…

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Q: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

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Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

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Q: Use the limit definition of partial derivatives to find f,(x, y) and f,(x, y). f(x, y) = x² – 8xy +…

A: We know, fx(x, y) = limh→0f(x+h, y) - f(x, y)h fy(x, y) = limh→0f(x, y+h) - f(x, y)h

Q: Find ü Partial olerivative i) heve l Sur face i isy Tamgent planes of function Gradient of F 4. 2.

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A: Partial derivative:

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A: Given fx,y=x-13y+22   To Find: The critical points of the above function for which the Second…

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Q: Prove that div curl v = 0 where the components of v have continuous second partial derivatives

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Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+…

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Q: How many second partial derivatives does f(a,b,c, d) have?

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Q: Determine whether the statement is true or false. If f has continuous partial derivatives of all…

A: since curl of divergence i.e

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Q: Find all 1st partials of the function z=xy/x^2+y^2

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Q: Suppose that f(x, y) is a smooth function and that its partial derivatives have the values, f.(-9,8)…

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Q: Compute the partial derivative fa(, 4, 2) of the function f(2,4, 2) = yz' + 2 – 2 vy + * +2 y. O…

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Q: ihe fcu,v, w) and its partial derivatives with respect tou and vand w and are Continous that u-メ-ツ…

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Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (7xy + 13xz + 17yz)²]. O…

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Q: Explain why the function is differentiable at the given point. f(x, y) = x³y?, (-2, 2) The partial…

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Q: Vf(r, y) = (300 – 12z? – 12y? , 18y? – 24.ry) - - -

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Q: Calculate the partial derivative f2(3,3,1), where f(x, y, z) = xyz. %3D

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Q: Let h(x, y) = , x = 41|12, y = 517t2. Use the Chain Rule to calculate the partial derivative. (Use…

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Q: tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=

A: Topic:- application of derivatives

Q: Compute the partial derivative of the function * with respect to z at the point (1,0, 7). Compute…

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Q: 4. Use the limit definition of partial derivative to find f, (x, y) and f, (x, y). a) f(x,y)=/x+y

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Q: sin (x³ + y*) x² + y² (x, y) # (0, 0) 66. f(x, y) = 0, (x, y) = (0, 0), af af and at (0, 0) ду

A: Formula Used: ∂f∂x(x0, y0)=limh→0f(x0+h, y0)-f(x0, y0)h∂f∂y(x0, y0)=limh→0f(x0, y0+h)-f(x0, y0)h…