y, thên thế total differential of and y O df = 11 dr + 16 dy O df = 15 dr + 19 dy O df = 12 dr +18 dy O df = 11 dr – 16 dy %3D

Q: Find the differential dy of the function y = 3x ' O a) dx b) 3x dr c) x 4 In(3) 3 d) dx e) 글x dx

A: We are given y =3x^(1/4)  To find dy just differentiate y with respect to x

Q: Find the differential dy. y = ex/2 dy =     Evaluate dy for x = 0 and dx = 0.05 dy =

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Q: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…

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Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : - O df = 32 dx + 4…

A: In total differential take the derivative of each terms, put the given values and simplify.

Q: Find the differential dy of the given function. y = V4 - x2 dy =

A:

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: Let y : 2x + 3x +4. Find the differential dy when x = 5 and dæ 0.3 Find the differential dy when x =…

A: Given, y=2x2+3x+4 Differentiating with respect to 'x', we get dydx=ddx2x2+3x+4=2×2x+3×1+0=4x+3…

Q: Use the differential dy to approximate Ay when x changes as indicated. y = V3x – 2; from x = 2 to x…

A: Topic - approximation Using derivatives

Q: Let y = 5x² + 5x + 3. Find the differential dy when x = 1 and dx = 0.1 %D %3D Find the differential…

A: Topic = Derivative

Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: (a) Find the differential dy. y = ex/4 dy = %3D (b) Evaluate dy for the given values of x and dx x =…

A: we have to derivative

Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: 1. Determine whether the following differential is exact or inexact: a) df = dx –dy %3D y b) df(x,y)…

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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: 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: (a) Find the differential dy of y = e#/5. (b) Evaluate dy for a = 0, dx = .1. (a) dy = dx (b) dy =

A: Solved below

Q: Find the differential of the function f(x, y) = re at (-2, 0). df =

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

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Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

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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) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: Given f(x, y) = 1æ²y then the total differential df = %3D

A: I have appended the formula used in the solution part.

Q: Q6. If w = y²z² + xy and x = t³ – 1; y=t² + 2; z= 3t , find the total dw at t = 2 dt differential

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Q: Find the differential dy. (a) y = xV10 - x dy = -2 (b) y = (1+x) ? dy =

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Q: (a) Find the differential dy of y = x² + 2x + 5. (b) Evaluate dy for x = 3, dx = 1/2. (а) dy 3 dx…

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Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

A: First differentiate with respect to x then find value at x=1 and dx=-0.1

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

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Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : df = 32 dx – 4 dy…

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Q: d?y dz? Find the two real root second order differential with for 6- + 5 dy = 6y dx O C1*e^(2x/3) +…

A: Solution:-  Given differential equation            6d2ydx2+5dydx=6y     Firstly rearrange  this as…

Q: (a) Find the differential dy of y= /4+ 5x. (b) Evaluate dy for æ = 0, dx = .04. (a) dy dx (b) dy =

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Q: (a) Find the differential dy. y = eX/5 dy = 4 (b) Evaluate dy for the given values of x and dx. x =…

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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: (a) Find the differential dy. y = V 24 + x2 dy = V 24 +x?

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Q: Find the differential dy. (a) y = xv8- x %3D dy %3D (b) y = (1+ x)7 dy

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Q: Find the differential of each function. (a) y = etan(rt) dy = (b) y = V2 + In(z) dy =

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: Which of these differentials is exact? (only one of them is exact) (1 – 2xy)dx + (x² + y²) dy O (22…

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

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Q: Find the differential dy of the given function. y = V4 - x2 dy

A: Consider the given function. The problem requires to find the differential dy of the given…

Q: Find the differential of the function. Z = e cos(2nt) dz = dx + dt

A: Given,

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: The total differential of g(x, y) = e*z²-y is at A(1,4) is %3D Select one: a. dg(A)=(8-1)e^(0) O b.…

A: Consider the following function: gx,y=e4x2-y Differentiate gx,y with respect to x taking y as…

Q: Find the differential of f(x, y) = vx2 + y³ at the point (1,2). df

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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: 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: Find the differential dy and (b) evaluate dy for the given values of x and dx. y=ex/10 , x = 0, dx…

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Q: Find the total differential. w = e7Y cos(4x) + z7 dw

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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: Use the differential dy to approximate Ay when x changes as indicated. y = V 3x – 2; from x = 2 to x…

A: