Let f be the R2 ? R function de ned byf(x; y) = ln xy2and let r be the R ? R2 function de ned byr(t) = (t2; et):(a) Determine the composite function f r. (Simplify your answer). (2)(b) Determine gradf(x; y) and r0(t). (3)(c) Determine the derivative function?f r0byi. di erentiating the expression obtained in (a) (2)ii. using the chain rule (Theorem 7.6.1). (2)Compare your answers. MAT2615_101.pdf - Adobe Acrobat Reader (64-bit)File Edit View Sign Window HelpHome ToolsBookmarks>MAT2615_101.pdf>INTRODUCTION> OVERVIEW OF MAT2615CURRICULUMTRANSFORMATION>LECTURER(S) ANDCONTACT DETAILSRESOURCESSTUDENT SUPPORTSERVICES> HOW TO STUDY ONLINE?MODULE SPECIFIC STUDYPLANMODULE PRACTICALWORK AND WORKINTEGRATED LEARNING> ASSESSMENTOTHER ASSESSMENTMETHODSCONCLUSION×> ADDENDUM A: SELFASSESSMENT TASK FORUNITS 1-3ADDENDUM B:ASSIGNMENTSX↓↓↓29 / 36Idetermine the derivative function or).9. Let f be the R2 - R function defined byf(x, y) = ln xy²and let y be the R- R2 function defined byсr(t) = (t²,et).(a) Determine the composite function for. (Simplify your answer).(b) Determine grad f(x, y) and r'(t).(c) Determine the derivative function (for)' byi. differentiating the expression obtained in (a)ii. using the chain rule (Theorem 7.6.1).Compare your answers.[14](3)NN[9][TOTAL: 85]Search 'Edit Text'IExport PDFⒸSelect PDF FileAdobe Export PDFConvert PDF Files to Wordor Excel OnlineMAT2615_101.pdfConvert toMicrosoft Word (*.docx)Document Language:English (U.S.) ChangeConvertSign InEdit PDFCreate PDFX×Convert, edit and e-sign PDFforms & agreements24 of 24 - ClipboardItem not Collected: Delete itemsto increase available space

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29 / 36 determine the derivative function (for). 9. Let f be the R²R function defined by f(x, y) = ln xy² and let r be the R-R² function defined by C r(t) = (t²,et). (a) Determine the composite function for. (Simplify your answer). (b) Determine gradf(x,y) and r'(t). (c) Determine the derivative function (for)' by i. differentiating the expression obtained in (a) ii. using the chain rule (Theorem 7.6.1). Compare your answers.

29 / 36 determine the derivative function (for). 9. Let f be the R²R function defined by f(x, y) = ln xy² and let r be the R-R² function defined by C r(t) = (t²,et). (a) Determine the composite function for. (Simplify your answer). (b) Determine gradf(x,y) and r'(t). (c) Determine the derivative function (for)' by i. differentiating the expression obtained in (a) ii. using the chain rule (Theorem 7.6.1). Compare your answers.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 15E

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