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Example 4 Video Example ) х2 +x - 3 Let y = Use the Quotient Rule to find y'. x3 + 8 Solution (x3 y' = + 8) 2 x +x - 3 (x² x° + 8 dx dx (x3 + 8)2 し) + 8) 2x + 1 - (x2 + x - 3) 3x 2 (x3 + 8)2 (x3 )-( 3x – 3r° + 9x² + 8) 2х — 1 4 (x3 + 8)2 -x4 – 2x3 + 9x? + 16x + 8 (x³ + 8)2

Example 4 Video Example ) х2 +x - 3 Let y = Use the Quotient Rule to find y'. x3 + 8 Solution (x3 y' = + 8) 2 x +x - 3 (x² x° + 8 dx dx (x3 + 8)2 し) + 8) 2x + 1 - (x2 + x - 3) 3x 2 (x3 + 8)2 (x3 )-( 3x – 3r° + 9x² + 8) 2х — 1 4 (x3 + 8)2 -x4 – 2x3 + 9x? + 16x + 8 (x³ + 8)2

Calculus: Early Transcendentals
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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A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into a nutrient broth, the culture grows at a rate proportional to its size. After 1.5 hours, the population has increased to 825. (a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.) P(t) = (b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.) P(4) = bacteria (c) Find the rate of growth (in bacteria per hour) after 4 hours. (Round your answer to the nearest whole number.) p'(4)= bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.) t = hr
Transcribed Image Text:A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into a nutrient broth, the culture grows at a rate proportional to its size. After 1.5 hours, the population has increased to 825. (a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.) P(t) = (b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.) P(4) = bacteria (c) Find the rate of growth (in bacteria per hour) after 4 hours. (Round your answer to the nearest whole number.) p'(4)= bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.) t = hr
Example 4 Video Example ) x2 + x - 3 Let y = Use the Quotient Rule to find y'. x3 + 8 Solution (43 y' = + 8). +x – 3 + x - 3) 8+ * (x³ + 8)2 (x3 + 8) 2х + 1 - (x2 + x - 3) 3x (x3 + 8)2 (x3 + 8) 2х - 1 3x4 – 3x + 9x? (x3 + 8)2 -x4 - 2x° + 9x2 + 16x + 8 (x3 + 8)2
Transcribed Image Text:Example 4 Video Example ) x2 + x - 3 Let y = Use the Quotient Rule to find y'. x3 + 8 Solution (43 y' = + 8). +x – 3 + x - 3) 8+ * (x³ + 8)2 (x3 + 8) 2х + 1 - (x2 + x - 3) 3x (x3 + 8)2 (x3 + 8) 2х - 1 3x4 – 3x + 9x? (x3 + 8)2 -x4 - 2x° + 9x2 + 16x + 8 (x3 + 8)2
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