Use the Chain Rule to find the indicated partial derivatives. дл მs дл z = x² + x²y, x = s + 2t-u, y = stu²; Əz əz Əz as' at au when s = 3, t = 4, u = 2 at Əz ди ||

Q: Find both partial derivatives дz ?х дz and for the equation exy + yz² = x³yz ду

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Q: (b) f(x) — хе*-у-z xex-y-z

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Q: Let-3x³ + 4y³ + 4z³ - 2xyz +428 = 0. Əz Əz Use partial derivatives to calculate and at the point…

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

A: Given function is rx,y=lnx+3y Differentiate partially rx,y=lnx+3y with respect to x…

Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y, x = s + 2t - u, y =: =…

A: Given the function z,x and y.

Q: Use the chain rule to find the indicated partial derivatives. x4. x² + x²y₁ x = s + 2t - u, y = stu…

A: To find partial derivatives of z w.r.t. s,t,u   Given z=x4+x2yx=s+2t-u and y=stu2

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. Z = 19xe…

A: Given, z=19 xey-9 ye-x

Q: Use the Chain Rule to find the indicated partial derivatives. P = √u2 + v2 + w², u = xey, v = yex, w…

A: Solution: P=u2+v2+w2   ............(1)Plug the value of u,v & wP =xey2+yex2+exy2

Q: Find all the first and second order partial derivatives of f(x, y) = −4 sin(2x + y) + 10 cos(x - y).…

A: Given:- fx,y=-4sin2x+y+10cosx-y

Q: Find all second order partial derivatives of the given functions f(x, y) = cos(2xy2 3x?y3)

A: Consider: fx,y=cos2xy2-3x2y3. Calculate: ∂2f∂x2. Apply chain rule: ∂u∂x=∂u∂v∂v∂x Let u=cos2xy2-3x2y3…

Q: Let w(z, y, z) = 1 + y² + z?, where z = 3', y = Int, and z = = et. Find I using the Chain Rule.

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Q: Use partial derivatives to find the coordinates which give the shortest distance from the point…

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Q: Use the chain rule to find the indicated partial derivatives. p+q N = -, p = u + vw, q = v + uw, r =…

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Q: y² + y²eG)° + 2x²•G° x': 2xye 6) Zaye*

A: The solution is given as

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: Use the Chain Rule to find the indicated partial derivatives x = s + 2t - u, y = stu²; when s = 4, t…

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Q: Use the chain rule to find the indicated partial z = x4 + x²y, x = s + 2t - u, y дz дz дz дя дt ди…

A: Given,                           z=x4+x2y, x=s+2t-u, y=stu2. To find the partial derivatives i.e…