Given S(x, y) = 8x + 3y − 6x² − 5y² – 7xy, answer the following questions: - (a) Find the first partial derivatives of S. Sz(x, y) = Sy(x, y) (b) Find the values of x and y that maximize S. Round to four decimal places as need x = =

Q: VI. Determine the following partial derivatives (it is essential to show the procedure) 1. fy 2.fy =…

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Q: For z = arctan(x² + y²): Compute all first and second order partial derivatives. Find the…

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Q: Q1. Find the derivatives of the following: 1. y = -x 2. s = 5t - 31s + 3 4x 3. у 3 4. w = 3z2 - 5. у…

A: Please find the detailed solution in below images

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Q: Find the first, second, and cross partial derivatives for the f(x, y) = 12x4 – 6x²y + 4xy3 %3D

A: Introduction: When a function is multivariable, we follow the partial derivative to find the…

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Q: 5. z = yex+x Iny xey-y lnx

A: Solution : z=yex+xln(y)xey-yln(x) zx=∂z∂x =∂ ∂ xyex+xlnyxey-ylnx-∂ ∂ xxey-ylnxyex+xlnyxey-ylnx2…

Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven,…

A: Given that, a rental truck costs $45.45 for a day plus 94c per mile.

Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y, x = s + 2t - u, y = stu²…

A: ∂s∂z​=∂t∂z​=∂u∂z​=0,  when s=3,t=1,u=5 Explanation:

Q: Find all the second partial derivatives. f(x, y) = x6y − 3x3y2

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