1. Find the first order partial derivatives: 2= In (x+ 2. Find the gradient of the function f(r.y) = In(r² + y² ) at the point(1,1). 3. Find the derivative of the function f(r, y, 2) = ry + yz + 2r at the point (1.-1,2) in the direction A = 31 + 6j – 2k.

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 4xyz + 6yz²…

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Q: S (x, y)=x'y² - 4y°

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Q: If z = f(x, y) has continuous second-order partial derivatives and x =r* +s² and y = 2rs , find a)…

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Q: g(x, Y, z) = /x² +z-2 + sin(xy – x²)

A: Let's find.

Q: Find the second order partial derivatives of f(x,y)=(3x+2y)^4

A: f(x, y ) = (3x + 2y)4 ∂f(x,y)∂x = 4 (3x +2y)3(3 +0) ∂f(x,y)∂x = 12 (3x + 2y)3 ∂2f(x,y)∂x2 = 12×3…

Q: (a) If f(1, y) = 1 cos y + ye", find the second-order partial derivatives.

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Q: Find the first partial derivatives with respect to x, y, and z. 3xz w = x + y aw Əx aw ду aw %3D Əz…

A: Here we need to find the partial derivatives of the given function with respect to x, y and z. While…

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 the partial derivatives of f(x, y) = 3x°y². (a) fz(x, y) = (b) fy(x, y) (c) fa(5, y) = (d)…

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Q: Compute the partial derivative of the function * f(x, y, z)= el-roos(y) +2e=1/(1+²)

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Q: Find all the second-order partial derivatives of the following function. h(x,y) — хеУ + 8у +4 %3D dx…

A: Solution :hx,y=xey+8y+4∂h∂x=ey∂h∂y=xey+8∂2h∂x2=∂∂x∂h∂x=∂∂xey=0∂2h∂y2=∂∂y∂h∂y=∂∂yxey+8=xey

Q: Find all second-order partial derivatives for the following. R(x,y) = 4x- 2x°y° +5x*y" Ryy Rxy Ryx

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Q: . Find all the second-order partial derivatives of the function z = f(x, y) = e2xe"

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Q: Use the chain rule to find the indicated partial derivatives. z = x* + xy, x = s + 2t – u, y = stu?…

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Q: Find all the second-order partial derivatives of the functions r(x, y) = ln (x + y)

A: rx+y=lnx+y Partially differentiating with respect to x, we get ∂r∂x=1x+y·∂x+y∂x…

Q: Use the chain rule to calculate the partial derivatives ∂f/∂t and ∂f/∂s. f(x, y) = (x2 + y2)esin xy…

A: c Given function is fx,y=x2+y2esinxy, where x=st and y=lnx+y. We have to find the ∂fdt and ∂fds by…

Q: Consider f(x, y, z) = 2x³ – 4y³ + 32³ – 7æ²y²z². Find all the first order partial derivatives fr,…

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Q: Calculate all four second-order partial derivatives of f(x, y) = 5x²y + 9xy³. fiz(x, y) fry (x, y) =…

A: To find out the double partial derivatives.

Q: Use the chain rule to find the indicated partial derivatives at p = 4,r = 3,0 = 0 and enter them…

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Q: .    Given y = (x, z) = 6x2 + 3xz4 where X(B, E, T) = B2 + 2E + TB Z(B, E, T) = (ETB)1 + B + E…

A: Given that,  y = (x, z) = 6x2 + 3xz4 where X(B, E, T) = B2 + 2E + TB Z(B, E, T) = (ETB)1 + B + E…

Q: Find the first partial derivatives of the function. Rx, y) = x?y® + 5xdy fx, v) =

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Q: Given that z = 2(r, y) and ze™" – a³z + In(x°z³) = 0, find the value of the partial derivative z, at…

A: We have to find the partial derivative zx at the point 1,0,1 where zexy-x3z+lnx2z3=0.

Q: Find the first partial derivatives of the following function. F(w,x,y,z) = 4w 4x + 9y + 5z Fw = Fx:…

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Q: Find the partial derivatives of the function f(r, y) = ryey fz(x, y) fy(1, y) = fzy (r, y) fyz (T,…

A: We need to find the different partial derivative of the function f(x, y)=xye1y

Q: Find the first partial derivatives and evaluate at the given point. Function Point f(x, y) = e*y²…

A: The given function isf(x, y) =exy2to find fx, fy  at (0, 6)

Q: Suppose f (x, y) = 4x? + 3y? . a. Calculate the partial derivatives of f. b. Suppose f (x, y) = 16 .…

A: Given that

Q: 10. Use the chain rule to find the indicated partial derivatives. (a) z = e"Y sin y, x = s+2t, y = ;…

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Q: Find all the second-order partial derivatives of the following function. 2х - у w = 3x2 + 3y w 2(2x°…

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Q: Please solve for  d^2f/dx^2=d^2f/dydx=d^2f/dy^2=d^2f/dxdy=

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Q: Evaluate the first partial derivatives of the function at the given point. f(x, y) = 9e* In(y); (0,…

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Q: Assume that all the given functions have continuous second-order partial derivatives. If z = f(x,…

A: Consider the equation x=r2+s2 therefore∂x∂s=2s y=2rs, therefore∂y∂s=2r

Q: Find all the second-order partial derivatives of the following function. w = 4y e 3x2 -y 24y (1 +…

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

A: Given that r(x,y) = ln(2x+3y) We need to calculate all the second order partial derivatives. The…

Q: 1 t3 4u p А (р, t, u) : pt2 u?

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Q: Find the partial derivatives of f(x, y) = 5x°y°. (a) fz(x,y) (b) fy(x,y) =[_ (c) f«(5, y) = (d)…

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Q: Calculate the first order partial derivatives and find and df dx dy f(x, y) = /x2 + y² f(x, y) = (x2…

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Q: Calculate all four second-order partial derivatives of f(x,y)=(5x+4y)e^y

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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 indicated partial derivatives: (a) fx(x, y) if f(x, y) = −3x^4 + 6y^2− 11 (b)fy(x, y) if…

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Q: Compute the four second-order partial derivatives of f(x, y) = ry? + 3x?e".

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Q: 다음 함수 /의 2계 편도함수를 모두 구하여라 (1) fx, y, 2) sin (xy) cos (vz)

A: As per Our guidelines we can solve maximum one question u can repost other's in next question

Q: Use the Chain Rule to evaluate the partial derivative g at the point (r, 0) = (2/2, 7) where g(x, y)…

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

Q: Find all the second-order partial derivatives of the function. r(x,y) = In (3x + y) дудх дхду dy? II…

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Q: Find the second partial derivatives of the function f(x,y) = x°y° + 2x°y. 1. 2. 3. dxdy a² f 4. dy?…

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Q: Find the partial derivatives of the function -lz + 2y 2 + 2y f(z, y) = S-(E, y) = fy(z,y) =

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Q: Evaluate the indicated partial derivatives. f(x, y) = 2a°ye*y af (1, 1) = af dy 2,(1,1) =

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Q: Find the first partial derivatives and evaluate at the given point. Function Point 2ху Vx? + y? f(x,…

A: To find the partial derivatives at the given points

Q: Find the indicated partial derivatives. f(x, y, z) = - i fy(9, 1, 7) + y + z fy(9, 1, 7) =

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Q: Use the Chain Rule to find the indicated partial derivatives. z = x* + xy³, az x = uv + w³, y=u+ vew…

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