Þ(x, y(x)) = x² + 5y¹(x), where y(x) = sin(x). Find different methods and compare: a) Substitute for y(x), and find the derivative. b) Use the chain rule for a function with two variables. dz using

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Consider the following function with two variables:
Þ(x, y(x)) = x² + 5y¹(x), where y(x)= sin(x). Find (()) using the following two
different methods and compare:
dx
a) Substitute for y(x), and find the derivative.
b) Use the chain rule for a function with two variables.
Transcribed Image Text:Consider the following function with two variables: Þ(x, y(x)) = x² + 5y¹(x), where y(x)= sin(x). Find (()) using the following two different methods and compare: dx a) Substitute for y(x), and find the derivative. b) Use the chain rule for a function with two variables.
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