Given f(x, y) = 12/8x* + 6y + 2xy°, find fa(x, y) = f,(x, y) =

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

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Q: The linear approximation at r = 0 to sin(2x) is A+ Bx where A is: and where B is:

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Find the differential dy. y = 5x2 / x-9       dy =

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Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

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Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: b- Yt dt + dBt dY; 1-t

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Q: (r, y, z) = sin 2x i + xz cos y j+ e*y iv F,

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Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: Using the substitutions X = u+2, y=w+2; dx = du, dy= dw, the DE with linear coefficients (x + y-…

A: Using the substitutions X=u+2, y=w+2; dx = du, dy=dw, the DE with linear coefficients (x+y-4) dx +…

Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: dy _ 4xy+5y² can be transformed into a seperable DE The DE: dx xy +3x2 in x and z by using the…

A: The solution is given as

Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Given f(x, y) = 11x²y then the total differential df = %3D 11xy dx + 11x² dy 2xy dx + x² dy 22xy dx…

A: The function is given by fx,y = 11x2y To evaluate : The expression of the total differential df

Q: Use the Chain Rule to find dz/dt. z - x2 + y2 + xy, x = sin(t), y - 2e Use the Chain Rule to find…

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Q: when (x, y, z) = (2, 2, 1). dt dz dy If x2 + y2 + z2 = 9, dx 8, and dt 4, find dt %3D %3D %3D dz dt

A: differentiate the given function with respect to 't' 2x dx/dt +2y dy/dt +2z dz/dt =0 Now substitute…

Q: use the chain rule to find dz/dt, where z=x sin y, x=t^5, and y=5t^2 please show steps

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Q: If f(z, y) = e" sin(4y) then: V f( – 1, 1) =

A: Given function is f(x, y) =e4xsin4y.  We have to find ∇f(1, -1 ). The vector differential operator ∇…

Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

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Q: at (s, t) = (0, 1) if ds z = 6x + y² tan (), x = e" – st, y = s² – f.

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Q: |dx + N(x,y)dy = 0 x² + y,

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Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: Given f(x, y) = 2e" sin(4y) v (0, then V %3D 2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: dz Use an appropriate form of the chain rule to find dt z = 4x°y³; x = tº, y = t" Enter the answer…

A: From the given problem: z=4x6y3 ; x=t8 , y=t7 Now apply the chain rule.…

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: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

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: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

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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: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

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Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: Given f(x, y) = 4e2" sin(2y) %3D then V f(0, 7) =

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Q: . Use fourth order Runga Kutta Method to find y at x=0.1, given that dy = 3e* + 2y , y(0) = 0 and h…

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: Use the chain rule to find dz/t. z = x² + y² + xy, x = sint, y = et

A: Here we will find dz/dt,

Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

A: We have to check whether the given differential equations are linear and homogeneous or not. A…

Q: Use the Chain Rule to Find dz/dt, where z=2xsiny, x=t^5, and y=3t^3.

A: Chain rule  dz/dt=(dz/dx)(dx/dt)+(dz/dy)(dy/dt)

Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

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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: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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