2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o Point)
2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o Point)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![1. Differentiate the following function:
\[ y = \frac{(\ln X \cdot \sin X)^3}{\cos 2X} \]
(10 points)
2. Use the fundamental derivative formula to differentiate the following at \( x = 2 \):
\[ g(x) = \frac{3x - 1}{2x + 1} \]
(10 points)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d6c3626-f5d1-4083-9c5f-3d056d67e7f7%2F7e3e9f5e-b09d-49f2-9f0f-8f55df0f623c%2Fov55nu4h_processed.png&w=3840&q=75)
Transcribed Image Text:1. Differentiate the following function:
\[ y = \frac{(\ln X \cdot \sin X)^3}{\cos 2X} \]
(10 points)
2. Use the fundamental derivative formula to differentiate the following at \( x = 2 \):
\[ g(x) = \frac{3x - 1}{2x + 1} \]
(10 points)
![## Mathematical Problems and Solutions
### Problem 6
**Evaluate the Integral:**
\[
\int e^x \sin x \, dx
\]
*(15 points)*
---
### Problem 7
**Optimization of Production for Profit Maximization:**
The profit \(P\) of a company depends on the number of a specific shoe product. The following equation relates the number of shoes to the profit:
\[
P(x) = 2 + 0.02x^3 - 0.001x^4
\]
Find the production quantity that maximizes the function for a maximum of 20 shoes.
*(20 points)*
---
In both problems, you will apply calculus principles to solve integrals and optimize functions for real-world applications of mathematics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d6c3626-f5d1-4083-9c5f-3d056d67e7f7%2F7e3e9f5e-b09d-49f2-9f0f-8f55df0f623c%2F1pldm9b_processed.png&w=3840&q=75)
Transcribed Image Text:## Mathematical Problems and Solutions
### Problem 6
**Evaluate the Integral:**
\[
\int e^x \sin x \, dx
\]
*(15 points)*
---
### Problem 7
**Optimization of Production for Profit Maximization:**
The profit \(P\) of a company depends on the number of a specific shoe product. The following equation relates the number of shoes to the profit:
\[
P(x) = 2 + 0.02x^3 - 0.001x^4
\]
Find the production quantity that maximizes the function for a maximum of 20 shoes.
*(20 points)*
---
In both problems, you will apply calculus principles to solve integrals and optimize functions for real-world applications of mathematics.
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