1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula for the second derivative of y is Faz F2-2Fry FaFy + FyyF2 d'y dx² F3 Y

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.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 28E
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1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then
a formula for the second derivative of y is
FxxF2 - 2Fxy FxFy + FyyF2
d²y
dx²
F3
Y
(Hint: This question really tests your understanding of the chain rule!)
Transcribed Image Text:1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula for the second derivative of y is FxxF2 - 2Fxy FxFy + FyyF2 d²y dx² F3 Y (Hint: This question really tests your understanding of the chain rule!)
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