Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

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Q: Let Compute dw Əs dw Ət -(-3,-4)= -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

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Q: Let Compute θω Əs δω Ət -(-3,-4) (-3,-4)= = w = -5xy + 4yz - xz, x = st, y = est, z = t²

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A: Jacobian of the function at a given point

Q: Let Compute θω Əs δώ Ət -(-3,-4) -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A: By chain rule, we will solve the problem.

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Q: Differentiate

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Q: et f(x, у, z) %3 ху + z', Р %3D (3, 9, 1

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Q: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = tan(u/v), u = 3s + 9t, v = 9s − 3t ∂z ∂s ∂z…

A: Here Z is a function of u and v. u and v are both functions of s and t.So, we can say that Z is a…