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Q1. Find the derivatives y(x)= dy/dx of functions y(x) listed below, simplify the answers, and plot the relevant graphs. Do it in 2 steps: (1) firstly, do not simplify y(x) before evaluation of y'(x) and simplify y'(x) after evaluation; (2) then, for verification, simplify y(x) and, after simplification, evaluate y(x) and compare it with the result of step (1). (Program Outcomes: PI-P4, P6-P8) (a) y(x) = x² (x-1)² (4 points) (1) Direct evaluation: y'(x)= (2) Simplify: y(x)= Verify: y'(x)= (b) y(x)= x²-1 x+1 (1) Direct evaluation: (2) Simplify: y(x)= (c) y(x) = sin²(x) y'(x)= y'(x) = Verify: y'(x)= (4 points) (2 points)

Q1. Find the derivatives y(x)= dy/dx of functions y(x) listed below, simplify the answers, and plot the relevant graphs. Do it in 2 steps: (1) firstly, do not simplify y(x) before evaluation of y'(x) and simplify y'(x) after evaluation; (2) then, for verification, simplify y(x) and, after simplification, evaluate y(x) and compare it with the result of step (1). (Program Outcomes: PI-P4, P6-P8) (a) y(x) = x² (x-1)² (4 points) (1) Direct evaluation: y'(x)= (2) Simplify: y(x)= Verify: y'(x)= (b) y(x)= x²-1 x+1 (1) Direct evaluation: (2) Simplify: y(x)= (c) y(x) = sin²(x) y'(x)= y'(x) = Verify: y'(x)= (4 points) (2 points)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q1. Find the derivatives y(x)= dy/dx of functions y(x) listed below, simplify the answers, and plot the relevant graphs. Do it in 2 steps: (1) firstly, do not simplify y(x) before evaluation of y'(x) and simplify y'(x) after evaluation; (2) then, for verification, simplify y(x) and, after simplification, evaluate y(x) and compare it with the result of step (1). (Program Outcomes: PI-P4, P6-P8) (a) y(x) = x² (x-1)² (4 points) (1) Direct evaluation: y'(x)= (2) Simplify: y(x)= Verify: y'(x)= (b) y(x)= x²-1 x+1 (1) Direct evaluation: (2) Simplify: y(x)= (c) y(x) = sin²(x) y'(x)= y'(x) = Verify: y'(x)= (4 points) (2 points)
Transcribed Image Text:Q1. Find the derivatives y(x)= dy/dx of functions y(x) listed below, simplify the answers, and plot the relevant graphs. Do it in 2 steps: (1) firstly, do not simplify y(x) before evaluation of y'(x) and simplify y'(x) after evaluation; (2) then, for verification, simplify y(x) and, after simplification, evaluate y(x) and compare it with the result of step (1). (Program Outcomes: PI-P4, P6-P8) (a) y(x) = x² (x-1)² (4 points) (1) Direct evaluation: y'(x)= (2) Simplify: y(x)= Verify: y'(x)= (b) y(x)= x²-1 x+1 (1) Direct evaluation: (2) Simplify: y(x)= (c) y(x) = sin²(x) y'(x)= y'(x) = Verify: y'(x)= (4 points) (2 points)
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