1 Po(x) = v2 3 P1(1) = : %3D "V 2 PĄ(2) = (3=² – 1) V P3(x) = ; (5x³ – 3r) /5 Write down the derivatives of each of those 4 functions. Yes, I'm literally asking you to just take a few derivatives. Don't make this hard. Now write each derivative in terms of the 4 polynomials. Some of them may be trivially easy to write down, like “This derivative is 0* Po(x)+0*Pi(x)+0*P2(x)+0*P3(x)."
1 Po(x) = v2 3 P1(1) = : %3D "V 2 PĄ(2) = (3=² – 1) V P3(x) = ; (5x³ – 3r) /5 Write down the derivatives of each of those 4 functions. Yes, I'm literally asking you to just take a few derivatives. Don't make this hard. Now write each derivative in terms of the 4 polynomials. Some of them may be trivially easy to write down, like “This derivative is 0* Po(x)+0*Pi(x)+0*P2(x)+0*P3(x)."
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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![### Transcription for Educational Website
**Polynomials and Derivatives Exercise**
Consider the polynomials defined as follows:
\[
P_0(x) = \frac{1}{\sqrt{2}}
\]
\[
P_1(x) = x \sqrt{\frac{3}{2}}
\]
\[
P_2(x) = \frac{1}{2} \left( 3x^2 - 1 \right) \sqrt{\frac{5}{2}}
\]
\[
P_3(x) = \frac{1}{2} \left( 5x^3 - 3x \right) \sqrt{\frac{7}{2}}
\]
**Instructions:**
1. Write down the derivatives of each of these four functions. The task is straightforward—just compute the derivatives.
2. Now, express each derivative in terms of the given polynomials \( P_0(x), P_1(x), P_2(x), \) and \( P_3(x). \) Some derivations may be simple to write, for example: "This derivative is \( 0 \cdot P_0(x) + 0 \cdot P_1(x) + 0 \cdot P_2(x) + 0 \cdot P_3(x). \)"
---
Make sure to perform the calculations carefully and present the derivatives in the simplest form possible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65ba51bd-93fe-4637-8f7c-e52d3fdaa23e%2F0d9064ce-2186-4027-af1b-2226bcce70b5%2Fjs8v4cp_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Website
**Polynomials and Derivatives Exercise**
Consider the polynomials defined as follows:
\[
P_0(x) = \frac{1}{\sqrt{2}}
\]
\[
P_1(x) = x \sqrt{\frac{3}{2}}
\]
\[
P_2(x) = \frac{1}{2} \left( 3x^2 - 1 \right) \sqrt{\frac{5}{2}}
\]
\[
P_3(x) = \frac{1}{2} \left( 5x^3 - 3x \right) \sqrt{\frac{7}{2}}
\]
**Instructions:**
1. Write down the derivatives of each of these four functions. The task is straightforward—just compute the derivatives.
2. Now, express each derivative in terms of the given polynomials \( P_0(x), P_1(x), P_2(x), \) and \( P_3(x). \) Some derivations may be simple to write, for example: "This derivative is \( 0 \cdot P_0(x) + 0 \cdot P_1(x) + 0 \cdot P_2(x) + 0 \cdot P_3(x). \)"
---
Make sure to perform the calculations carefully and present the derivatives in the simplest form possible.
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