Find the total derivative matrix Df at (2, y) = (1, 1) for the following function 8 y! +5 z2y3" 5 1 3 y? f (r, y) : In Df use the first column for derivatives with respect to æ and the second column for derivatives with respect to y. Enter the matrix Df using the equation editor below. Use the palette to choose the appropriate size matrix.

Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

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Q: Consider f(z, y, 2) = 4x² – 2y + 4° – 6z²y2. Find all the first order partial derivatives fa. fy…

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Q: compute the first-order partial derivatives. z = ln(x2 + y2)

A: Consider the given function z=lnx2+y2 We have to find the first-order partial derivative. ∂z∂x, ∂z∂y…

Q: If z = (x + y)e and x = u? + v² and y = u? – v², find the following partial derivatives using the…

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Q: .    Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to…

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Q: Find the first partial derivatives of the function. w = In(x + 2y + 7z) %3D aw Əx aw ду aw %3D az II…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Which of the following is the gradient vector of the function f(x, y) = 3x ln 3y - 2x²y at point (1,…

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Q: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

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Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

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Q: Find the gradient of the function at the given point. In(x² – y) – 8, (3, 8) Vz(3, 8) =

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Q: Find the partial derivative at point(u,v)=(-4,0) of w=ln(xa+yb+za),x=uevsin u y=uevcos u, z=uev,…

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Q: Obtain the orthogonal trajectories of xy = C and compute for the positive value of y at the point…

A: Solution

Q: Use the limit definition of partial derivatives to compute the partial derivative of the function…

A: Given query is to find partial derivative using definition.

Q: Find all the second partial derivatives of the function a) f(x,y) = x* – 3x²y³. %3D | b) f(x,y) =…

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Q: Find the gradient of the function at the given point. In(x² – y) - 9, (3, 8) z = Vz(3, 8) =

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Q: Find the gradient of the function z = ln(x2 − y) /(x − 4), at the given point     (2, 3)

A: To find the gradient differentiate z partially with  respect to x and y. Given function  z=lnx2-yx-4…

Q: Find the first partial derivatives of the function. w = In(x + 3y + 6z) 3 %3D ду x + 3y + 2z aw dz…

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Q: Find the first partial derivatives of the function. u = 8xY/z du %3D du %3D ay du %3D az

A: Please refer the attached image for complete solution.

Q: Find the gradient of the function at the given point. In(x² – y) – 6, (2, 3) z = Vz(2, 3) =

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Q: Find the gradient of the function at the given point. In(x² – y) – 6, (3, 8) z = Vz(3, 8) =

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Q: Find the first partial derivatives with respect to x, y, and z. 5xz W = x + y aw ax aw ду aw az

A: Find  first partial derivative.

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: ○ (2x,-1,-1/2) (2x₂ O…

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Q: Use chain rule to find given x² + 2y² + z² and x os (st), y %3D Cos

A: Solve the following

Q: Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to (-1, 0,…

A: The gradient of f(x, y, z) is:

Q: Let -2r+5y - z + 3xyz + 163 = 0. Use partial derivatives to calculate and at the point (1, - 3, 2).…

A: For find ∂z∂x, differentiate partially the given function with respect to 'x' taking y as constant…

Q: Find the total derivative matrix Df at (x, y) = (1, 1) for the following function 2 y5 +2 a?y5 23 +…

A: Let's find.

Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

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Q: The function f whose gradient vector is vf(x,y) = (xIn(v + 7), 7x + y + 7> has two critical points…

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Q: Find the value of at the point (1, 1, 1) if the equation xy+ z°x – 2yz = 0 defines z as a function…

A: Given equation, xy+z3x-2yz=0

Q: Find the first partial derivatives of the function. z = (8x + 7y)5 Əz ax az %3D Əy

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Q: Find the gradient of the function w = 1/(√1 − x2 − y2 − z2),  and the maximum value of the…

A: The given vector is:

Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: In(3x² – 2y + 4z³); x = t², y = t³ , z =t-l. Find the maximum derivative the function f(x, y) = x² –…

A: Given that w=ln3x2-2y+4z3 The objective is to find dwdt By chain rule,…

Q: Write the matrix of partial derivatives of f(p, 0, ¢) = (p cos 0 sin ø, p cos 4)

A: Here in the given question, find the partial derivative of the given matrix:…

Q: Use the Chain Rule to calculate the partial derivatives д(т, у) — sin (т? + у?), х— 4и — v, у — —…

A: Given g(x, y)=sin(x2+y2) ,x= 4u-v and y=-(2u+2v)

Q: Find the second order Partial Derivatives of the functions with respect to each variable 3) r(x, y)…

A: Second order partial derivative will be  ∂2r∂x2 , ∂2r∂y2 , ∂2r∂x∂y , ∂2r∂y∂x

Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

A: Given

Q: Compute the matrix of partial derivatives of the following function. f(x, y, z) = (x + z, y - 5z, x…

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Q: If z = sin(x/y) and x = ln (u) and y = v^4, find the partial derivatives of z with respect to u and…

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Q: Find the first partial derivatives of the function. W = In(x + 3y + 6z) 1 x + 3y + 6z aw 3 ду х+ Зу…

A: Given :W=ln x+3y+6zTo determine∂w∂x,∂w∂y and ∂w∂z

Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

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Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: Find the gradient of the function In(x² − y) – 1, X Vz(2, 3) = Z at the given point. (2, 3)

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Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: Find the gradient of the function at the given point. In(x² - y) - 9, (2, 3) = Z Vz(2, 3) =

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Q: Find the first partial derivatives with respect to x, y, and z. 7xz W = x + y aw ax aw ду aw az ||

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Q: Find all the second-order partial derivatives of the function. r(x,y) = In (2x + 3y)

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Q: Find the total derivative matrix Df at (x, y) = (1, 1) for the following function %3D | 6 y5 +9 z²y5…

A: The solution of given matrix is written in step2 and step3.

Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

A: Given functions are