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4. Let f: R² → R be given by f(x, y) = x² + y² and c: R → R² be given by c(t) = (t, e¹). Then (f o c)'(t) is a real valued function of one real variable (with denoting the derivative). Compute (foc)'(0) directly and by using the chain rule.

4. Let f: R² → R be given by f(x, y) = x² + y² and c: R → R² be given by c(t) = (t, e¹). Then (f o c)'(t) is a real valued function of one real variable (with denoting the derivative). Compute (foc)'(0) directly and by using the chain rule.

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.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 48E
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4. Let f: R² → R be given by f(x, y) = x² + y² and c: R → R² be given by c(t) = (t, et). Then (f o c)'(t) is a real valued function of one real variable (with denoting the derivative). Compute (foc)'(0) directly and by using the chain rule.
Transcribed Image Text:4. Let f: R² → R be given by f(x, y) = x² + y² and c: R → R² be given by c(t) = (t, et). Then (f o c)'(t) is a real valued function of one real variable (with denoting the derivative). Compute (foc)'(0) directly and by using the chain rule.
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