Math Problem Statement

For the following composite​ function, find an inner function uequals​g(x) and an outer function yequalsf ​(u) such that yequals​f(g(x)). Then calculate StartFraction dy Over dx EndFraction . yequalscosine StartFraction 8 x Over 5 EndFraction Question content area bottom Part 1 Select the correct choice below and fill in the answer box to complete your choice. A. StartFraction dy Over dx EndFraction equalsStartFraction d Over du EndFraction ​(u)timesStartFraction d Over dx EndFraction left parenthesis StartFraction 8 x Over 5 EndFraction right parenthesis equals    enter your response here B. StartFraction dy Over dx EndFraction equalsStartFraction d Over du EndFraction left parenthesis StartFraction 8 u Over 5 EndFraction right parenthesis timesStartFraction d Over dx EndFraction ​(cosine x​)equals    enter your response here C. StartFraction dy Over dx EndFraction equalsStartFraction d Over du EndFraction ​(cosine u​)timesStartFraction d Over dx EndFraction left parenthesis StartFraction x Over 5 EndFraction right parenthesis equals    enter your response here D. StartFraction dy Over dx EndFraction equalsStartFraction d Over du EndFraction ​(cosine u​)timesStartFraction d Over dx EndFraction left parenthesis StartFraction 8 x Over 5 EndFraction right parenthesis equals

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Composite Functions
Trigonometric Functions
Chain Rule

Formulas

y = cos(8x/5)
dy/dx = (dy/du) * (du/dx)
dy/du = -sin(u)
du/dx = 8/5

Theorems

Chain Rule

Suitable Grade Level

Grades 11-12