dz Find the total derivative given: a) z = f(x,y) = 2x + xy-y² where x = g(y) = 3y² b) z = f(x, y) = 6x²-3xy = 2y² where x = g(y) = ² y c) z = f(x, y) = (x+y)(x-2y) where x = g(y) = 2-7y Find the total derivative given: a) z=x²-8xy-y³ where x = 3t and y-1-t b) z = f(x, y, t) where x = a = bt and y = c + dt Find the partial total derivatives W₁, and W, if W = ax² + bxy + cu where x = au + Bv and y = yu
dz Find the total derivative given: a) z = f(x,y) = 2x + xy-y² where x = g(y) = 3y² b) z = f(x, y) = 6x²-3xy = 2y² where x = g(y) = ² y c) z = f(x, y) = (x+y)(x-2y) where x = g(y) = 2-7y Find the total derivative given: a) z=x²-8xy-y³ where x = 3t and y-1-t b) z = f(x, y, t) where x = a = bt and y = c + dt Find the partial total derivatives W₁, and W, if W = ax² + bxy + cu where x = au + Bv and y = yu
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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Transcribed Image Text:dz
dy
Find the total derivative given:
a) z=f(x,y) = 2x + xy-y² where x = g(y) = 3y²
b) z=f(x, y) = 6x²-3xy = 2y² where x = g(y) = ²/
c) z = f(x,y) = (x+y)(x-2y) where x = g(y) = 2-7y
dz
Find the total derivative given:
a) z = x² - 8xy - y³ where x = 3t and y-1-t
b) z = f(x, y, t) where x = a = bt and y = c + dt
Find the partial total derivatives W₂, and W₂, if W = ax² + bxy + cu where x = au + Bv and y = yu
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