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1. Find the first partial derivatives of the following functions: a. f(x, y, z) = 3x²/² b. f(x, y) = arctan(y/x) at (2,3)

1. Find the first partial derivatives of the following functions: a. f(x, y, z) = 3x²/² b. f(x, y) = arctan(y/x) at (2,3)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve problem 1 with explanation please. Thank you
1. Find the first partial derivatives of the following functions: a. f(x, y, z) = 3.x/ b. f(x, y) = arctan(y/x) at (2,3) 2. Use implicit differentiation to find az/ax and dz/day for yz + xlny = 3. Use the first principles to find f(x, y) and f(x, y) if f(x, y) = xy². 4. Find the differential of the function B^² = x²e-²x³² 5. Use the Chain Rule to find az/as and dz/dt if z = = (sin(2r+1))(In 8), 6. Use a tree diagram to write out the Chain Rule (assume all functions are dif r=r(x, y), s = s(x, y), and t = 1(x, y)
Transcribed Image Text:1. Find the first partial derivatives of the following functions: a. f(x, y, z) = 3.x/ b. f(x, y) = arctan(y/x) at (2,3) 2. Use implicit differentiation to find az/ax and dz/day for yz + xlny = 3. Use the first principles to find f(x, y) and f(x, y) if f(x, y) = xy². 4. Find the differential of the function B^² = x²e-²x³² 5. Use the Chain Rule to find az/as and dz/dt if z = = (sin(2r+1))(In 8), 6. Use a tree diagram to write out the Chain Rule (assume all functions are dif r=r(x, y), s = s(x, y), and t = 1(x, y)
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