Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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d/dx [pi^pi]
![In this image, we have an expression involving calculus notation. It reads as follows:
\[ \frac{d}{dx} \left[ \pi^{\pi} \right] \]
This expression represents the derivative of a constant term, which is \(\pi^\pi\), with respect to \(x\).
**Explanation:**
1. **Derivative**: The symbol \(\frac{d}{dx}\) denotes taking the derivative with respect to \(x\).
2. **Constant Term**: \(\pi^\pi\) is a constant value, where \(\pi\) (pi) is a mathematical constant approximately equal to 3.14159, and here it is raised to the power of itself.
Since \(\pi^\pi\) does not depend on \(x\) (it's a constant), its derivative with respect to \(x\) is zero.
Thus, the derivative is:
\[ \frac{d}{dx} \left( \pi^\pi \right) = 0 \]
This is an important concept in calculus, highlighting that the derivative of any constant value with respect to a variable is zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3d10f68-bc93-449e-9d46-249fabbb429f%2F44abc39a-695b-4f12-8010-1aa046e5dd14%2Fv78xseo_processed.png&w=3840&q=75)
Transcribed Image Text:In this image, we have an expression involving calculus notation. It reads as follows:
\[ \frac{d}{dx} \left[ \pi^{\pi} \right] \]
This expression represents the derivative of a constant term, which is \(\pi^\pi\), with respect to \(x\).
**Explanation:**
1. **Derivative**: The symbol \(\frac{d}{dx}\) denotes taking the derivative with respect to \(x\).
2. **Constant Term**: \(\pi^\pi\) is a constant value, where \(\pi\) (pi) is a mathematical constant approximately equal to 3.14159, and here it is raised to the power of itself.
Since \(\pi^\pi\) does not depend on \(x\) (it's a constant), its derivative with respect to \(x\) is zero.
Thus, the derivative is:
\[ \frac{d}{dx} \left( \pi^\pi \right) = 0 \]
This is an important concept in calculus, highlighting that the derivative of any constant value with respect to a variable is zero.
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