Find f and f, and evaluate each at the given point. y' ху f(x, y) = (9, -9) %3D 1. X - y fy(X, Y) = %3D 5,(x, y) = %3D fx(9, -9) = %3D f(9, -9) %3D

Q: 4. Find the orthogonal trajectories of the given family of curves. y = cx'.

A: Solution:-              y=cx3 →          1              Diff. w.r.t x            ⇒dydx=3cx2…

Q: Find the Partial Derivatives of the functions with respect to each variable X+y 6) f(x,y) = -у' -1…

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Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

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Q: Find the first partial derivatives with respect to x, y, and z and evaluate each at the given point.…

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Q: Q2: Find the Partial Derivatives of the functions with respect to each variable x and y and z: 4.…

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: Find the first partial derivatives of the function. f(x, t) = tªe¬x %3D

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Q: The integrating factor of the LDE y' = x - 2ycotx is

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Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

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Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Find the four second partial derivatives of the following function. f(x,y) = ln (3x2 + 4y2 + 7)…

A: We have to find

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: Q1: Find partial derivatives of the function with respect with each variable 1) f(x, y)=2x² − 3y – 4…

A: Solution

Q: Find the partial derivative of f(x, y) 8x - 2xy2 + y3 with respect to x at the point (2, 1, 61).

A:

Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

Q: Find the value of at the point (1,1,1) if the equation 3xy +z°x-2yz = 2 defines z as a function of…

A: First do the partial differential in both the sides and then separate ∂z∂x and then put the value…

Q: (b) Find the first order partial derivative af and for the function f(x, y) = x/y –x²y+ y²

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Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

Q: Find the value of ∂x/∂z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x…

A: Given equation is xz+ylnx-x2+4=0. Given point is 1,-1,-3. Partial derivative of given equation with…

Q: Compute the indicated partial derivative. g(x, y, z) = x³y^z° 9xxyz =

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Q: Find the first partial derivatives and evaluate at the given point. Function Point f(x, y) = Invxy…

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Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: Find f, and f,. f(x, y) = 13x In xy

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Q: Compute the indicated partial derivative. g(x, y, z) = x³y^z° 9xxyz %3D

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Q: Find the linearization L(x)of the function at a .

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Q: Find fz and fy- f(z, 9) = [" 9eª dt f.(x, y) = f,(x, y) =

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Q: Find the Partial Derivatives of the functions with respect to each variable 2) f(x,y) = (x² – 1)y+…

A: Explanation of the answer is as follows

Q: 9. If f(x, y) = +, then find the first and second order partial derivatives.

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: Find the Partial Derivatives of the functions with respect to each variable 4) f(x,y)=\x² + y?

A: We have  f(x,y)=x2+y2 So we can write f(x,y)=(x2+y2)12 And we know that ∂(xn)∂x=nxn-1

Q: Find the linearization of the function f (x) = x³ at x = 1. L(x) = Using this linearlization, ƒ…

A: Answer is in next step.

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: Find the partial derivative. 3p f (p, q) = e af

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Q: 8. Find the orthogonal trajectories of y = cx CX

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Q: Find the second-order partial derivative fxx ( x , y ) of the function f ( x , y ) = x 4 y 4 - sqrt…

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Q: If f(x, y) = x3 + y4, what is the partial derivative of f with respect to х? .A fx = 4x3 || .B fx =…

A: The objective is  to find the partial derivative with respect to x.

Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: Find the Partial Derivatives of the functions with respect to each variable 4) f(x, y) = x +y²

A: Partial derivative means when we take derivative with respect to one variable than other variable…

Q: Q2: Find Partial derivative of the function with the respect with each variable f(x, y) = (x² - 1)(y…

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Q: 10. Use the Chain Rule to find the indicated partial derivative if ax F = Vu? + v2 + w², u = xe, v =…

A: F=u2+v2+w2To find ∂F∂x

Q: 5. Find the second partial derivatives of f(x, y) = x²y³ + 3y?

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Q: 6) Find the orthogonal trajectories for the given families of curve 3x - y = c.

A: To find orthogonal trajectory first differentiate with respect to x then remove constant then put…

Q: Find L(x) (Linearization function), given f(x) = ev2x at the value a = 2.

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Q: find the partial derivative of the function with respectto each variable. h(x, y, z) = sin (2πx + y…

A: We have to find the partial derivative of the function with respect to each variable   The given…

Q: 8. Find the orthogonal trajectories of y cx

A: