+ find the derivate
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
Find the derivate using a graph as final answer
![**Calculus: Finding the Derivative**
To further your understanding of calculus, let's dive into the concept of finding derivatives. A derivative represents the rate at which a function is changing at any given point, and it is fundamental in the study of calculus due to its broad range of applications in various scientific fields.
In the image, you are asked to "find the derivative." The request is accompanied by a graph featuring a curve and coordinate axes, as illustrated below:
```
|
| /
| /
| /
----------------
| /
| /
|/
```
**Steps to Find the Derivative:**
1. **Identify the Function:**
- Analyze the curve provided in the graph to determine the function it represents, denoted as \( y = f(x) \).
2. **Apply Differentiation Techniques:**
- Use appropriate rules of differentiation (such as the power rule, product rule, quotient rule, or chain rule) to find the derivative of the function \( f(x) \).
3. **Interpret the Derivative:**
- The derivative, denoted as \( f'(x) \) or \(\frac{dy}{dx}\), signifies the slope of the tangent to the curve at any point \( x \). This value indicates the rate of change of the function at that specific point.
Let's use an example for better clarity:
If the curve represents the function \( y = x^2 \), then the steps to find its derivative are as follows:
1. **Function Identification:**
- \( y = x^2 \)
2. **Differentiate:**
- Apply the power rule: \(\frac{d}{dx} [x^n] = nx^{n-1}\)
- Therefore, \( \frac{dy}{dx} = 2x \)
3. **Derivative Interpretation:**
- For \( y = x^2 \), the derivative \( \frac{dy}{dx} = 2x \) indicates that at any point \( x \), the slope of the tangent to the curve is \( 2x \).
Remember, practice is key to mastering differentiation. Begin with simple functions and gradually work up to more complex ones.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c7b497-dac7-4855-b923-2e60bbc73063%2F326535f3-cabc-4291-a42c-44cad863c2f8%2F6tr72bj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculus: Finding the Derivative**
To further your understanding of calculus, let's dive into the concept of finding derivatives. A derivative represents the rate at which a function is changing at any given point, and it is fundamental in the study of calculus due to its broad range of applications in various scientific fields.
In the image, you are asked to "find the derivative." The request is accompanied by a graph featuring a curve and coordinate axes, as illustrated below:
```
|
| /
| /
| /
----------------
| /
| /
|/
```
**Steps to Find the Derivative:**
1. **Identify the Function:**
- Analyze the curve provided in the graph to determine the function it represents, denoted as \( y = f(x) \).
2. **Apply Differentiation Techniques:**
- Use appropriate rules of differentiation (such as the power rule, product rule, quotient rule, or chain rule) to find the derivative of the function \( f(x) \).
3. **Interpret the Derivative:**
- The derivative, denoted as \( f'(x) \) or \(\frac{dy}{dx}\), signifies the slope of the tangent to the curve at any point \( x \). This value indicates the rate of change of the function at that specific point.
Let's use an example for better clarity:
If the curve represents the function \( y = x^2 \), then the steps to find its derivative are as follows:
1. **Function Identification:**
- \( y = x^2 \)
2. **Differentiate:**
- Apply the power rule: \(\frac{d}{dx} [x^n] = nx^{n-1}\)
- Therefore, \( \frac{dy}{dx} = 2x \)
3. **Derivative Interpretation:**
- For \( y = x^2 \), the derivative \( \frac{dy}{dx} = 2x \) indicates that at any point \( x \), the slope of the tangent to the curve is \( 2x \).
Remember, practice is key to mastering differentiation. Begin with simple functions and gradually work up to more complex ones.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
