If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O df- 16 dz +20 dy O df- 16 dz - 20 dy O df – 20 dz+23 dy

Q: F(x, y) = (8xy° + 3)i+ (12x²y² + 2e2")j is conservative by finding a potential function f for F, and…

A: Given that, Fx,y=8xy3+3i+12x2y2+2e2yj⋯⋯(1) C: rt=2sin5ti+2tπsin85tj 0≤t≤π2S Let, F=Mi+Nj Where,…

Q: Assume that x and y are functions of t. If y = x² + 4x and dx/dt = 4, find dy/dt when x = 1. dy dt…

A: Solve the following

Q: sa (0, ") : If f(1, y) = 18e* cos z + 5 cot y, then the total differential of f at (0, O df = 18 dr…

A: Total derivative

Q: f(x, y) = 7x – 5y (a) Find f(4, 5) and f(4.1, 5.05) and calculate Az. f(4, 5) = f(4.1, 5.05) = %3D…

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Q: Let f(x, y) = (2.8x – 2.7y) /3r+ 0.5y. The formula of the differential df at M(2.2, 0.5) is df = dx…

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Q: Let w(z, y, 2) = x² + y² + z² where z = sin(7t) , y = cos(7t), z = e'. dz dy dw by first finding dt…

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Q: Let z = f(x,y) = 2x² – xy. a) Find the differential dz. b) Compute the value of dz if (x, y) changes…

A: Here we use formula of partial derivative to find dz We have,         dz=∂z∂xdx+∂z∂ydy

Q: dw Use the Chain Rule to find dt w = 7x°y°z,x = 2t, y = cos(4t), z = tsint %3D 7xy°(12yz -…

A: see 2nd and 3rd step.aa

Q: 1. Verify that (t) = et, y(t) = e' satisfies the system %3D dx 3y3 dt dy y, dt %3D

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Q: w In(x2 + y2 +z?), x = ue" sin u, y = ue" cos u and z ue", using chain rule at the point (u, v) =…

A: Given w=lnx2+y2+z2x=uevsinuy=uevcosuz=uev

Q: Find f(2, 1) and f(2.1, 1.05) and calculate Δz, and use the total differential dz to approximate Δz.…

A: Given

Q: If f(x, y) = 4x? – 8y, then the total differential of f at a = 1 and y = -2 is : O df = 8 dx – 32 dy…

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Q: If f(z, y) = 22e cos z+9 cot y, then the total differential of f at (0, ) (0. is: O df = 22 dz + 18…

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Q: Given f(x, y) = 4x²y then the total differential df %3D O 4xy dx + 4x² dy O 8xy dx + 4x² dy None of…

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Q: Let z = f(x,y)= x^3+ xy+ y^4    (a)  Use differentials to estimate Δz as x changes from 1 to 1.05…

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Q: Find the differential dy. (a) y = xV7-x dy (b) y = (1+x) dy

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Q: (A) Find div (e grad u xf) at (2,1,0) where x-y and =(x²+1)i+sec¯¹(x² −y)j + 3y²z. k YZ 11=

A: What is grad, div and curl: Gradient, divergence and curl are important in vector calculus. Gradient…

Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If f(x, y) = 17e* cos x + 6 cot y, then the total differential of ƒ at ( 0, ÷) i : O df = 17 dx + 12…

A: f(x,y)=17e-xcos x +6 cot y

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: The total differential of the function: Z= x*e3y. dz =e3Y dx +3x "dy. „A O 4 3y dz = 4x3e3Y dx +3x…

A: the given function is: z=x4e3y we have to find the total differential of the given function.

Q: Write the differential dw in terms of the differentials of the independent variables. w = f(x.y.z) =…

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Q: Use the Chain Rule to find dw/dt. In(Vx² + y² + z² ), x = 3 sin(t), y = 5 cos(t), z = 6 tan(t) W =…

A: We have to find the derivative  using chain rule.

Q: Find the differential dy. (a) y = xv10 – x %3D dy %3D (b) y = (1+ x) 6 dy

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Q: Let y = V5- z. Find the differential dy whenz= 2 and dr = 0.1 %3D Find the differential dy whenz= 2…

A: y=5-x

Q: Given: f(x,y) = 2x²y³ and the points (1,2) and (1.1, 2.05) a.) Find f(1,2) and f(1.1,2.05). Then…

A: Here we want to find ∆Z using the function values and total differential.

Q: If f(r, y) = 3x2 – 8y, then the total differential of f at z = 1 and y=-2 is: %3D O df = 6 dx + 32…

A: we can find the total differential as below using the properties of partial derivative

Q: If f(x, y) = 19e CoS I +7 cot y, then the total differential of fat (0.) is: 4 O df= 19 dr + 14 dy…

A: Let the function is f(x, y)=19e-xcos x+7cot y Total differential is defined as df=fx(x, y) dx+fy(x,…

Q: Given f(x, y) = 8x²y then the total differential df ,2, O 8xy dx + 8x² dy O 16xy dx + 8x² dy O 16x…

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Q: Let y = (x + 3). %3D Find the differential dy when z = 2 and dz = 0.2 Find the differential dy when…

A: Given:  y=(x2+3)5  Differentating y with respect to xdydx=ddx(x2+3)5Using differential power rule…

Q: dy dy dt * dx dt dx Ex3: Use the chain rule to express: in terz dx dy t2 a) y = and t = v2x +1 %3D…

A: Given rule of derivative  dydx=dydt×dtdx

Q: Write the differential dw in terms of the differentials of the independent variables. w =…

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Q: Let f(x, y) = (2.8x – 2.7y) /3x + 0.5y. The formula of the differential df at M(2.2, 0.5) is | df =…

A: Given: Let, fx, y=2.8x-2.7y3x+0.5y To Find: To find the formula of the differential df at M2.2,…

Q: If f(z,y) = 3z² - 8y, then the total differential of f at z =1 and y = -2 is: %3D O df = 6 dz + 32…

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Q: If f(1, y) = 17e cos z+ 9 cot y, then the total differential of f at (0,) is O df = -17 dr + 18 dy O…

A: Given that:-     fx,y=17e-xcosx+9coty  we know that total differential is =     df=fxdx+fydy…

Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

A: Explained below

Q: Find the differential of the function f (x, y, z) = sin x?y³z4. %3D O 2xy³z* cos a?y³ zªd« O 2xy®z*…

A: Given f(x,y,z)=sin(x2y3z4)=ddx(sin(x2y3z4))We know that sin(x)'=cos(x)=cos(y3z4x2)*ddx(x2y3z4)

Q: If f(r, y) = 22e cos z +2 cot y, then the total differential of f at (0, ) %3D is: O df = 22 da +4…

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Q: If f(x, y) = 16e * cos x + 4 cot y, then the total differential of f at (0, is: O df = 16 dæ – 8 dy…

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Q: dy dæ at x = 2 if y = 3x + 5 and dt Find - 2. %3D %3D - dt dy %3D dt

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Q: If f(x, y) = 22e¯ª cos x + 4 cot y, then the (0, is total differential of f at - O df = 22 dæ + 8 dy…

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Q: If f(x, y) = 4x²y+7xy°, then the total differential of f at x = 1 and y = 1 is : %3D O df = 15 dx –…

A: Use formula of total differential

Q: Let w(x, y, z) = x2 + y? + z2 where x = sin( – 2t) , y = cos( – 8t), z = e". 9t dw dx dy dz…

A: To find the derivative using chain rule

Q: If f(x, y) = 2x2 – 9y, then the total differential of f at x = 1 and y = -2 is : O df = 4 dx - 36 dy…

A: Given: fx,y=2x2-9y2 To determine: The total differential of f at x=1 and y=-2.

Q: Let z = f(x, y) = 2xy + x. Write the differential dz in terms of x, y, dx, and dy. %3D

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Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…

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Q: Use the Chain Rule to find dz / dt or dw/ dt.(odd) z = xy3 - x2y, x = t2 + 1, y = t2 -1

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Q: Find the differential of the function, y = v1+x O 1) dy = Vx+1 O 2) dy = 2vx +1 O 3) dy = %3D 1 O 4)…

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Q: Find the total differential of the function f(2, y,) : y + z' df = dæ + dy + dz (y+2)* (y+2)* y+z dz…

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