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Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x,y) = yF (#) for {(x, y) = R², y ‡ 0}. Show that x² ƒxx = y² fyy.

Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x,y) = yF (#) for {(x, y) = R², y ‡ 0}. Show that x² ƒxx = y² fyy.

Calculus For The Life Sciences
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
Section4.4: Derivatives Of Exponential Functions
Problem 37E: Use graphical differentiation to verify that ddxex=ex.
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3. Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x, y) = yF for {(x, y) = R², y ‡ 0}. Show that x² ƒxx = y² fyy.
Transcribed Image Text:3. Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x, y) = yF for {(x, y) = R², y ‡ 0}. Show that x² ƒxx = y² fyy.
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