Let f be the R 2 − R function defined by f (x, y) = ln xy and let r be the R − R 2 function defined by r (t) = e t , t . (a) Determine the composite function f ◦ r. (Simplify your answer.) (2) (b) Determine gradf (x, y) and r 0 (t). (3) (c) Determine the derivative function (f ◦ r) 0 by (i) differentiating the expression obtained in (a), (2) (ii) using the Chain Rule (Theorem 7.6.1). (2) Compare your answers.

Let f be the R 2 − R function defined by f (x, y) = ln xy and let r be the R − R 2 function defined by r (t) = e t , t . (a) Determine the composite function f ◦ r. (Simplify your answer.) (2) (b) Determine gradf (x, y) and r 0 (t). (3) (c) Determine the derivative function (f ◦ r) 0 by (i) differentiating the expression obtained in (a), (2) (ii) using the Chain Rule (Theorem 7.6.1). (2) Compare your answers.

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 35E

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