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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Question
![**Problem Statement:**
Evaluate \(\frac{d}{dx} \left( 3x^2 + 10 \right) e^{-x}\) at \(x = 0\).
**Solution:**
\[
\left. \frac{d}{dx} \left( 3x^2 + 10 \right) e^{-x} \right|_{x=0} =
\]
**Explanation/Notes:**
The problem requires finding the derivative of the function \((3x^2 + 10) e^{-x}\) with respect to \(x\) and then evaluating this derivative at \(x = 0\). This involves using the product rule of differentiation because the function is a product of two simpler functions: \(3x^2 + 10\) and \(e^{-x}\).
The empty box on the right is where the numerical answer will be entered after performing the differentiation and substitution of \(x = 0\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2057a955-5437-4cdf-84c2-2ad34f3379f9%2F10910988-04ed-4c5e-a822-4f8b14851cc2%2Fmyn45hf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Evaluate \(\frac{d}{dx} \left( 3x^2 + 10 \right) e^{-x}\) at \(x = 0\).
**Solution:**
\[
\left. \frac{d}{dx} \left( 3x^2 + 10 \right) e^{-x} \right|_{x=0} =
\]
**Explanation/Notes:**
The problem requires finding the derivative of the function \((3x^2 + 10) e^{-x}\) with respect to \(x\) and then evaluating this derivative at \(x = 0\). This involves using the product rule of differentiation because the function is a product of two simpler functions: \(3x^2 + 10\) and \(e^{-x}\).
The empty box on the right is where the numerical answer will be entered after performing the differentiation and substitution of \(x = 0\).
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