3. Consider the function u(x, y) = f(3x +4y) + e2(3x-4y) + 3x - 4y and let s = 3x +4y and t = 3x - 4y. Given that f(s) is a twice differentiable function prove that 4 ди дх 3 ди ду 82u дудх = = 12 (f" (s) + 2).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 36E
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3. Consider the function u(x, y) = f(3x + 4y) + e2(3x-4y) + 3x - 4y and let s = 3x +4y and
t = 3x - 4y. Given that f(s) is a twice differentiable function prove that
ди
дх
ди
ду
02 u
дудх
=
= 12 (ƒ"(s) + 2).
Transcribed Image Text:3. Consider the function u(x, y) = f(3x + 4y) + e2(3x-4y) + 3x - 4y and let s = 3x +4y and t = 3x - 4y. Given that f(s) is a twice differentiable function prove that ди дх ди ду 02 u дудх = = 12 (ƒ"(s) + 2).
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