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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![The equation shown is a derivative expression:
\[
\frac{d}{dx} f(x) = e^{x^2} + x \ln \left( \sqrt{1 - x^3} \right)
\]
This equation represents the derivative of a function \( f(x) \) with respect to \( x \). It includes the following components:
1. \( e^{x^2} \): This is an exponential function with the base \( e \) raised to the power of \( x^2 \).
2. \( x \ln \left( \sqrt{1 - x^3} \right) \): This part of the equation includes a natural logarithm. The expression inside the log is the square root of \( 1 - x^3 \). This term is multiplied by \( x \).
Understanding and working with this equation requires knowledge of differentiation, exponential functions, logarithms, and algebraic manipulation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14c5f959-c92b-4b44-a2d8-262629dd1768%2Fca4be274-f3fe-46cd-9f28-9c5c41067421%2Fgy6dl1_processed.png&w=3840&q=75)
Transcribed Image Text:The equation shown is a derivative expression:
\[
\frac{d}{dx} f(x) = e^{x^2} + x \ln \left( \sqrt{1 - x^3} \right)
\]
This equation represents the derivative of a function \( f(x) \) with respect to \( x \). It includes the following components:
1. \( e^{x^2} \): This is an exponential function with the base \( e \) raised to the power of \( x^2 \).
2. \( x \ln \left( \sqrt{1 - x^3} \right) \): This part of the equation includes a natural logarithm. The expression inside the log is the square root of \( 1 - x^3 \). This term is multiplied by \( x \).
Understanding and working with this equation requires knowledge of differentiation, exponential functions, logarithms, and algebraic manipulation.
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