Let f(x, y, z) = x*y+ + z* and r = st, y = st, and z = (a) Calculate the primary derivatives af (b) Calculate as ds (C) Use the Chain Rule to compute af ds In (C) express your answer in terms of the independent variables t, s || || ||

Q: Find the first partial derivatives of the function. w = In(x + 4y + 8z) Əw ax aw ду aw II II II

A: Given, w= ln(x+4y+8z)

Q: The first order partial derivative of f(x, y)= x' with respect to 'x' is а. ух-1 yx- b. (у-1)x' c.…

A: For partial derivative with respect to x, we take y as a constant.

Q: a) z=x² In (x y²) b) z=4 cos(x-3y)

A: As we know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Chain rule:…

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: 3: Find all the second-order partial derivatives of the functions a) f(x. y) = x + y + xy

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Q: Find all the second-order partial derivatives of the functions w = x2 tan (xy)

A: Consider the given function: Here the objective is to find all second-order partial derivatives of…

Q: Find all the first and second order partial derivatives of f(x, y) = - Vã+ In y. x3

A: While finding the partial derivative of a multivariable function, if we have to find the partial…

Q: 9. Find all second order partial derivatives for the following functions: a) z = xe-2y + x In(y) + y…

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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 first partial derivatives of the function. w = In(x + 2y + 5z) aw ax aw ду aw Əz II II

A: w= ln(x+2y+5z) To find: Partial derivative with respect to x,y,z.

Q: dw as a function of t, both by using the chain rule and by expressing w in terms of t and…

A: Given query is to find the derivative of the expression.

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

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Q: Let f(x, y, z) = x°y* + z* and æ = s³t2, y = st, and z = st. (a) Calculate the primary derivatives…

A: Given the functions

Q: 29. f(x, у) %3D 3 (1, 2) y

A:

Q: Calculate all four second-order partial derivatives of the function f(x, y) = x² + 2xy + y² You must…

A: take the partial derivative with respect to x

Q: Using the second fundamental theorem of calculus and chain rule, compute dz t dt. t+1 2x

A:

Q: Let f(x, y, z) = x'y³ + z³ and st, y = st?, x = and (a) Calculate the primary derivatives af af dy…

A:

Q: compute the first-order partial derivatives.  z = e−x2−y2

A: Given,z = e−x2−y2We have to evaluate ∂z∂x and ∂z∂y

Q: Find all the first and second order partial derivatives of z for the following function: z = x2 – xy…

A:

Q: 9. Find all second order partial derivatives of the functions given below. (a) f(x,y) = x*y³ + x²y³…

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Q: Find the first partial derivatives of the following function. g(x,y) = cos ° (x°y³) ag

A: I have used chain rule for derivative

Q: Find the first partial derivatives of the following function. 2s +t f(s,t) = 4s-t

A:

Q: 9. Find all second order partial derivatives of the functions given below. (a) f(x,y) = x*y³ + x²y³…

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Q: Find the first partial derivatives of the function w = sin a cos B.

A:

Q: Find all the first and second order partial derivatives of f(x, y) = -1 sin(2a +y) - 10 cos(x - y).…

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Q: Find all second-order partial derivatives of the function given below. g(x, y) =x2+y+cosy+ysinx

A: For finding second order partial derivatives we need to find first order partial derivatives…

Q: Find all second-order partial derivatives of the function f(x,y) = x + xy – 5x³ + In(x² + 1).

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Q: Find the first and second-order partial derivatives of f (x, y) = x - 9x²y+ 3xy af b)

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Q: Confirm that the mixed second-order partial derivatives of f are the same. f (x, y) = 4 ln(x² +y²)…

A: This question is based on Partial differentiation.

Q: compute the first-order partial derivatives. z = x /x2 + y2

A: For a function in several variables partial derivative with respect to one variable is calculated by…

Q: Find all second-order partial derivatives of the given functions: (c) h(x,y) = In (x² + y)

A: Given; h(x,y)=ln(x2+y).

Q: Let f(x, y, z) = 6xy- z, x = 3r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

A:

Q: 2) Find all the second-order partial derivatives of the functions: a. f(x, y) = tan (-)

A:

Q: Find the first partial derivatives of the function. R(p, q) = tan(pq") R,(P, q) = Rop, q) =

A:

Q: Find all the second-order partial derivatives of the functions g(x, y) = cos x2 - sin 3y

A: Find all the second-order partial derivatives of the functions g(x, y) = cos x2 - sin 3y

Q: Find all the first and second order partial derivatives of the function f(x, y) = x sin y + y sin x…

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Q: Find all the second order partial derivatives of the function : f(x, y) = = In 3xy + sin 2xy +…

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Q: Find all the second order partial derivatives of the given function. f (x, y) = In(x²y – x) %3D

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Q: Confirm that the mixed second-order partial derivatives of f are the same. f(r, y) = 3 ln(x² + y³)…

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Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ f(x,y)= fx(x,y)= Of(x,y)= f₂(x, y) =…

A: We need to find partial derivative.

Q: Find all the second order partial derivatives of the given function. f (x, y) = x² + y – ex+y

A: Here we need to find the second order partial derivatives…

Q: Find the first partial derivatives of the function. R(p, q) = tan-1(pq5) Rp(p, q) Ralp, a)

A:

Q: Let f(x, y, z) = 8xy – z², x = 7r cos(0), y = cos²(0), z = 3r. Use the Chain Rule to calculate the…

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Q: Find the first partial derivatives of the function and evaluate them at the indicated point f (x, y)…

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Q: 27. Find the first partial derivatives of b. f(u, v) = tan-(4)

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Q: Let ƒ(x, y) = 3x2 + y3.a. Compute ƒx and ƒy.b. Evaluate each derivative at (1, 3).c. Find the four…

A: Given:                      f(x, y)=3x2+y3   To determine:               a) The partial derivatives…

Q: Find all second partial derivatives of Z e

A:

Q: 9. Find all second order partial derivatives for the following functions: a) z = xe-2 + xIn(y) + y…

A: f(x,y,z) = x cos(y+2z)∂f∂x = cos(y+2z) ddx(x)∂f∂x = cos(y+2z)∂2f∂x2=ddx[cos(y+2z)]∂2f∂x2 = 0

Q: Find all the second-order partial derivatives of the functions w = x sin (x2y)

A: Given function is w=xsinx2y. To find all the second-order partial derivatives of the function.…

Q: Calculate the derivatives of all orders: f'(x), f"(x), f"'(x), f(4)(x), f(x) = e3x - 1 f(x) = 3e3r-1…

A: We use chain rule to find these derivatives