Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

Q: If y = Vx(3 – x)², show that- dy (3-х) (3-4x) Find the x coordinates of %3D dx all points on y =…

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Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: If z = xy + 3xy', where x = sin 2t and y = cos t, find dz/dt when t = 0.

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Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

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Q: Find the differential of the function w=x^5sin⁡(y^5z^4) dw=  dx+  dy+  dz

A: Differential of a function is simply the derivative of a function. Also, d(uv) = u.dv + du.v

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

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

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Q: Let y = f(x), where f(x) = Vx + 4. Find the differential of the function. dy =

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Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

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Q: dy dz Find at z = 1 if y = 4z +4 and = 2. dt

A: Given: y=4x2+4

Q: Find the total differential. z = 10x5, y7 dz =

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Q: Assume that y=2x and dx/dt =4. Find dy/dt . dy/dt

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Q: 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…

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Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

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Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: Compute /. x² dx dy dz, where E = {(x, y, z) : x² + y² < 1,0 < z < 1}.

A: To evaluate ∬∫Ex2dxdydz, Where E is the region E=x,y,z:x2+y2≤1, 0≤z≤1.

Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t² at t=1

A: I have solved the problem with two methods.Final solution is in the box.

Q: Differentiate: y = /16 – z² – 4 arccos() e+4 y' = Oy= Oy- %3D

A: Given that : y = √(16 - x2) - 4arccos(x/4). We find derivative of this function (y).       Here i…

Q: Suppose that x=x(t) and y=y(t) are both functions of t. If x2 + y2 =17, and dx/dt=2 when x=4 and…

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Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: w =sec (xyz) - Yx +y+z

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Q: Find aff dy dx² for f(x, y) = exy

A: I have done solution in detail....step by step....go through the solution

Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: If L = sqrt(x2 + y2,) dx/dt = -1, and dy/dt = 3, find dL/dt when x = 5 and y = 12.

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Q: dy 2. sec²y secx dx ;y(0)=0

A: The given differential equation is dysec2y=dxsecx and y(0)=0

Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

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Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

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Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: Find the differential dy. y = ex/2   dy=

A: Here the given expression is y = ex/2. Apply the chain rule:

Q: e following integral: 23 8xyz dz dx dy. 120

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Q: 2sin(y)cos(y) sint(y)+costy) dy

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Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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Q: Use the Chain Rule to find dz/dt. z = x2 + y?, x = cost + sin t, y = cos t – sin t. -

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Q: The Integrating Factor for the DE y dx = (ye' – 2x)dy %3D is: -2y レマ None of These 2y

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Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

A: Draw the sketch, as follows: Since the ball is moving 25° North of "Straight Down" direction, its…

Q: Assume that y=5x and dx/dt = 8 find dy/dt

A: Differentiate by chain rule : →f(g(x))dx = d(f(x))d(g(x))×d(g(x))dx.

Q: Find the total differential. z = 5x³y4 dz =

A: Solve the given

Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given by…

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Q: f 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to…

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Q: Find differential of the function y = (x² + 3)°. dy = dx. When x = 4 and dx 0.05, compute the…

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Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: What is the integrating factor of (ry + y) dr + (r + 2y-1) dy %3D

A: Given xy+y2dx+(x+2y-1)dy=0Compare above differential equation with…

Q: Find the total differential. z = 6x *y5 iz

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Q: Find dy/dx: 1. у%3D Jo = San* sec? t dt

A: A detailed solution is given below

Q: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…

Q: What is the integrating factor of the nonexact DE (4xy + 3y – x) de + æ (x + 2y) dy = 0?

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Q: Can i get help step by step please

A: Given

Q: Let X = In(sint),y=1+cost Find dy/dx .

A: We can find the answer as below