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Math Calculus Calculus For The Life Sciences

Find the derivative of each function. v = ln ⁡ u u 3

Find the derivative of each function. v = ln ⁡ u u 3

Solution Summary: The author explains that the derivative of the function v=mathrmlnu3 can be derived by the following rule.

Calculus For The Life Sciences

Calculus For The Life Sciences

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 4.5, Problem 16E

Find the derivative of each function.

v = ln ⁡ u u 3

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Chapter 4.5, Problem 15E

Chapter 4.5, Problem 17E

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Chapter 4 Solutions

Calculus For The Life Sciences

Ch. 4.1 - YOUR TURN If ft=1t, find f't.Ch. 4.1 - Prob. 2YT Ch. 4.1 - YOUR TURN If ht=-3t2+2t+5t4-7, find h't.Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...

Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Which of the following describes the derivative...Ch. 4.1 - Which of the following describes the derivative...Ch. 4.1 - Explain the relationship between the slope and the...Ch. 4.1 - Prob. 26E Ch. 4.1 - Find each derivative. Dx9x-1/2+2x3/2 Ch. 4.1 - Find each derivative. Dx8x4-3x3 Ch. 4.1 - Prob. 29E Ch. 4.1 - Find each derivative. f'3 if fx=x39-7x2 Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - Prob. 35E Ch. 4.1 - Find all points on the graph of fx=x3+9x2+19x-10...Ch. 4.1 - Prob. 37E Ch. 4.1 - In Exercises 37-40, for each function find all...Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - At what point on the graph of fx=-5x2+4x-2 is the...Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - In Exercises 43-46 of section 1.4, the effect of a...Ch. 4.1 - Show that, for any constant k, ddxfxk=f'xk.Ch. 4.1 - Prob. 50E Ch. 4.1 - Cancer Insulation workers who were exposed to...Ch. 4.1 - Prob. 52E Ch. 4.1 - Insect Mating Patterns In an experiment testing...Ch. 4.1 - Prob. 54E Ch. 4.1 - Bighorn Sheep The cumulative horn volume for...Ch. 4.1 - Brain Mass The brain mass of a human fetus during...Ch. 4.1 - Prob. 57E Ch. 4.1 - Body Mass Index The body mass index BMI is a...Ch. 4.1 - Prob. 59E Ch. 4.1 - Prob. 60E Ch. 4.1 - Prob. 61E Ch. 4.1 - Prob. 62E Ch. 4.1 - Prob. 63E Ch. 4.1 - Dogs Human Age From the data printed in the...Ch. 4.1 - Prob. 65E Ch. 4.1 - Prob. 66E Ch. 4.1 - Prob. 67E Ch. 4.1 - Prob. 68E Ch. 4.1 - Prob. 69E Ch. 4.1 - Prob. 70E Ch. 4.1 - Prob. 71E Ch. 4.1 - Prob. 72E Ch. 4.1 - Postal Rates U.S postal rates have steadily...Ch. 4.1 - Money The total amount of money in circulation for...Ch. 4.1 - Prob. 75E Ch. 4.2 - YOUR TURN Find the derivative of y=x3+74-x2.Ch. 4.2 - Prob. 2YT Ch. 4.2 - YOUR TURN Find Dx5x-32x+73x+7.Ch. 4.2 - Prob. 1E Ch. 4.2 - Prob. 2E Ch. 4.2 - Prob. 3E Ch. 4.2 - Prob. 4E Ch. 4.2 - Prob. 5E Ch. 4.2 - Prob. 6E Ch. 4.2 - Prob. 7E Ch. 4.2 - Prob. 8E Ch. 4.2 - Prob. 9E Ch. 4.2 - Prob. 10E Ch. 4.2 - Prob. 11E Ch. 4.2 - Prob. 12E Ch. 4.2 - Prob. 13E Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 16E Ch. 4.2 - Prob. 17E Ch. 4.2 - Prob. 18E Ch. 4.2 - Prob. 19E Ch. 4.2 - Prob. 20E Ch. 4.2 - Prob. 21E Ch. 4.2 - Prob. 22E Ch. 4.2 - Prob. 23E Ch. 4.2 - Prob. 24E Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 26E Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 28E Ch. 4.2 - Prob. 29E Ch. 4.2 - Prob. 30E Ch. 4.2 - Find the error in the following work....Ch. 4.2 - Prob. 32E Ch. 4.2 - Find an equation of the line tangent to the graph...Ch. 4.2 - Find an equation of the line tangent to the graph...Ch. 4.2 - Prob. 35E Ch. 4.2 - Prob. 36E Ch. 4.2 - Prob. 37E Ch. 4.2 - Prob. 38E Ch. 4.2 - Prob. 39E Ch. 4.2 - For each function, find the values of x in which...Ch. 4.2 - Prob. 41E Ch. 4.2 - Growth Models In Exercise 52 of section 1.5, the...Ch. 4.2 - Bacteria Population Assume that the total number...Ch. 4.2 - Work/Rest Cycles Murrells formula for calculating...Ch. 4.2 - Optimal Foraging Using data collected by zoologist...Ch. 4.2 - Cell Traction Force In a matrix of cells, the cell...Ch. 4.2 - Prob. 47E Ch. 4.2 - Cellular Chemistry The release of a chemical...Ch. 4.2 - Prob. 49E Ch. 4.2 - Memory Retention Some psychologists content that...Ch. 4.2 - Prob. 51E Ch. 4.2 - Prob. 52E Ch. 4.3 - YOUR TURN For the functions in Example 1, find fg0...Ch. 4.3 - YOUR TURN Let fx=2x-3 and gx=x2+1. 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Prob. 31E Ch. 4.3 - Prob. 32E Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 35E Ch. 4.3 - Prob. 36E Ch. 4.3 - Prob. 37E Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 41E Ch. 4.3 - Prob. 42E Ch. 4.3 - Prob. 43E Ch. 4.3 - Consider the following table of values of the...Ch. 4.3 - Prob. 45E Ch. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - Prob. 49E Ch. 4.3 - Prob. 50E Ch. 4.3 - Katie and Sarah are working on taking the...Ch. 4.3 - Margy and Nate are working on taking the...Ch. 4.3 - Prob. 53E Ch. 4.3 - Oil Pollution An oil well off the Gulf Coast is...Ch. 4.3 - African Wild Dog The African wild dog is currently...Ch. 4.3 - Thermal Inversion When there is a thermal...Ch. 4.3 - Prob. 57E Ch. 4.3 - Calcium Usage To test an individuals use of...Ch. 4.3 - Drug Reaction The strength of a persons reaction...Ch. 4.3 - Extinction The probability of a population going...Ch. 4.3 - Candy The volume and surface area of a jawbreaker...Ch. 4.3 - Prob. 63E Ch. 4.3 - Prob. 64E Ch. 4.3 - Prob. 65E Ch. 4.3 - Prob. 66E Ch. 4.4 - YOUR TURN 1 Find dy/dx for a. y=43x, b. y=e7x3+5 Ch. 4.4 - Prob. 2YT Ch. 4.4 - Prob. 3YT Ch. 4.4 - YOUR TURN 4 The quantity in grams of a radioactive...Ch. 4.4 - Prob. 1E Ch. 4.4 - Prob. 2E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 4E Ch. 4.4 - Prob. 5E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 10E Ch. 4.4 - Prob. 11E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 13E Ch. 4.4 - Prob. 14E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 16E Ch. 4.4 - Prob. 17E Ch. 4.4 - Prob. 18E Ch. 4.4 - Prob. 19E Ch. 4.4 - Prob. 20E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 25E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 28E Ch. 4.4 - Prob. 29E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 31E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 33E Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 35E Ch. 4.4 - Prob. 36E Ch. 4.4 - Use graphical differentiation to verify that...Ch. 4.4 - Prob. 38E Ch. 4.4 - Population Growth In section 2.1, Exercise 37, the...Ch. 4.4 - Minority Population In Section 2.1, Exercise 39,...Ch. 4.4 - Insect Growth The growth of a population of rare...Ch. 4.4 - Prob. 43E Ch. 4.4 - Whooping Cranes Based on data from the U.S. Fish...Ch. 4.4 - Prob. 45E Ch. 4.4 - Prob. 46E Ch. 4.4 - Mortality The percentage of people of any...Ch. 4.4 - Breast Cancer It has been observed that the...Ch. 4.4 - Arctic Foxes The age-weight relationship of female...Ch. 4.4 - Prob. 50E Ch. 4.4 - Ayrshire Dairy Cattle The researchers from the...Ch. 4.4 - Cutlassfish The cutlassfish is one of the most...Ch. 4.4 - Prob. 53E Ch. 4.4 - Dialysis One measure of whether a dialysis patient...Ch. 4.4 - Medical Literature It has been observed that there...Ch. 4.4 - Prob. 56E Ch. 4.4 - Prob. 57E Ch. 4.4 - Prob. 58E Ch. 4.4 - Prob. 59E Ch. 4.4 - Prob. 60E Ch. 4.4 - Radioactive Iron Researchers found that the...Ch. 4.4 - Prob. 62E Ch. 4.4 - Prob. 63E Ch. 4.4 - Prob. 64E Ch. 4.4 - Habit Strength According to work by the...Ch. 4.4 - Prob. 66E Ch. 4.4 - Electricity In a series resistance-capacitance DC...Ch. 4.4 - Prob. 68E Ch. 4.4 - Prob. 69E Ch. 4.5 - YOUR TURN Find the derivative of fx=log3x.Ch. 4.5 - Prob. 2YT Ch. 4.5 - Prob. 3YT Ch. 4.5 - Find the derivative of each function. y=ln8x Ch. 4.5 - Prob. 2E Ch. 4.5 - Prob. 3E Ch. 4.5 - Prob. 4E Ch. 4.5 - Find the derivative of each function. y=ln4x2-9x Ch. 4.5 - Find the derivative of each function. y=ln-8x3+2x Ch. 4.5 - Find the derivative of each function. y=lnx+5 Ch. 4.5 - Prob. 8E Ch. 4.5 - Prob. 9E Ch. 4.5 - Prob. 10E Ch. 4.5 - Prob. 11E Ch. 4.5 - Prob. 12E Ch. 4.5 - Prob. 13E Ch. 4.5 - Find the derivative of each function. y=xln2-x2 Ch. 4.5 - Prob. 15E Ch. 4.5 - Find the derivative of each function. v=lnuu3 Ch. 4.5 - Prob. 17E Ch. 4.5 - Prob. 18E Ch. 4.5 - Find the derivative of each function. y=3x2lnx Ch. 4.5 - Prob. 20E Ch. 4.5 - Prob. 21E Ch. 4.5 - Find the derivative of each function. y=lnx-3 Ch. 4.5 - Find the derivative of each function. y=lnlnx Ch. 4.5 - Prob. 24E Ch. 4.5 - Prob. 25E Ch. 4.5 - Prob. 26E Ch. 4.5 - Prob. 27E Ch. 4.5 - Find the derivative of each function. py=lnyey Ch. 4.5 - Prob. 29E Ch. 4.5 - Prob. 30E Ch. 4.5 - Prob. 31E Ch. 4.5 - Find the derivative of each function. y=log4x-3 Ch. 4.5 - Prob. 33E Ch. 4.5 - Prob. 34E Ch. 4.5 - Prob. 35E Ch. 4.5 - Find the derivative of each function. y=log74x-3 Ch. 4.5 - Find the derivative of each function....Ch. 4.5 - Find the derivative of each function....Ch. 4.5 - Prob. 39E Ch. 4.5 - Find the derivative of each function. z=10ylogy Ch. 4.5 - Prob. 41E Ch. 4.5 - Find the derivative of each function. fx=lnxex+2 Ch. 4.5 - Prob. 43E Ch. 4.5 - Prob. 44E Ch. 4.5 - Prob. 45E Ch. 4.5 - Prob. 46E Ch. 4.5 - Prob. 47E Ch. 4.5 - Use a graphing calculator to sketch the graph of...Ch. 4.5 - Prob. 49E Ch. 4.5 - Prob. 50E Ch. 4.5 - Prob. 51E Ch. 4.5 - Prob. 52E Ch. 4.5 - Prob. 53E Ch. 4.5 - Prob. 54E Ch. 4.5 - Prob. 55E Ch. 4.5 - This exercise shows another way to derive the...Ch. 4.5 - Prob. 57E Ch. 4.5 - Population Growth Suppose that the population of a...Ch. 4.5 - Body Surface Area There is a mathematical...Ch. 4.5 - Prob. 60E Ch. 4.5 - Prob. 61E Ch. 4.5 - Fruit Flies A study of the relation between the...Ch. 4.5 - Prob. 63E Ch. 4.5 - Poverty The passage of the Social Security...Ch. 4.5 - Richter Scale The Richter scale provides a measure...Ch. 4.5 - Prob. 66E Ch. 4.6 - YOUR TURN Find the derivative of y=5sin3x4.Ch. 4.6 - YOUR TURN Find the derivative of y=2sin3x.Ch. 4.6 - Prob. 3YT Ch. 4.6 - Prob. 4YT Ch. 4.6 - Prob. 5YT Ch. 4.6 - Prob. 6YT Ch. 4.6 - Prob. 1E Ch. 4.6 - Prob. 2E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 4E Ch. 4.6 - Prob. 5E Ch. 4.6 - Prob. 6E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 8E Ch. 4.6 - Prob. 9E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 11E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 13E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 15E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 17E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 19E Ch. 4.6 - Prob. 20E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 23E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 25E Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 27E Ch. 4.6 - Prob. 28E Ch. 4.6 - Prob. 29E Ch. 4.6 - In Exercises 27-32, recall that the slope of the...Ch. 4.6 - Prob. 31E Ch. 4.6 - In Exercises 27-32, recall that the slope of the...Ch. 4.6 - Find the derivative of cotx by using the quotient...Ch. 4.6 - Prob. 34E Ch. 4.6 - Verify that the derivative of cscx is -cscxcotx....Ch. 4.6 - Prob. 36E Ch. 4.6 - Prob. 37E Ch. 4.6 - Carbon Dioxide Levels At Barrow, Alaska,...Ch. 4.6 - Prob. 39E Ch. 4.6 - Sound If a string with a fundamental frequency of...Ch. 4.6 - Prob. 41E Ch. 4.6 - Revenue from Seasonal Merchandise The revenue...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Prob. 10CR Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Prob. 12CR Ch. 4.CR - Prob. 13CR Ch. 4.CR - Prob. 14CR Ch. 4.CR - Prob. 15CR Ch. 4.CR - Prob. 16CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 19CR Ch. 4.CR - Prob. 20CR Ch. 4.CR - Prob. 21CR Ch. 4.CR - Prob. 22CR Ch. 4.CR - Prob. 23CR Ch. 4.CR - Prob. 24CR Ch. 4.CR - Prob. 25CR Ch. 4.CR - Prob. 26CR Ch. 4.CR - Prob. 27CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 29CR Ch. 4.CR - Prob. 30CR Ch. 4.CR - Prob. 31CR Ch. 4.CR - Prob. 32CR Ch. 4.CR - Prob. 33CR Ch. 4.CR - Prob. 34CR Ch. 4.CR - Prob. 35CR Ch. 4.CR - Prob. 36CR Ch. 4.CR - Prob. 37CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 39CR Ch. 4.CR - Prob. 40CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 42CR Ch. 4.CR - Prob. 43CR Ch. 4.CR - Prob. 44CR Ch. 4.CR - Prob. 45CR Ch. 4.CR - Prob. 46CR Ch. 4.CR - Prob. 47CR Ch. 4.CR - Prob. 48CR Ch. 4.CR - Prob. 49CR Ch. 4.CR - Prob. 50CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 52CR Ch. 4.CR - Prob. 53CR Ch. 4.CR - Prob. 54CR Ch. 4.CR - Prob. 55CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 57CR Ch. 4.CR - Prob. 58CR Ch. 4.CR - Prob. 59CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 61CR Ch. 4.CR - Prob. 62CR Ch. 4.CR - Prob. 63CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 65CR Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 68CR Ch. 4.CR - Consider the following table of values of the...Ch. 4.CR - Consider the following table of values of the...Ch. 4.CR - Prob. 71CR Ch. 4.CR - Prob. 72CR Ch. 4.CR - Find the slope of the tangent line to the given...Ch. 4.CR - Prob. 74CR Ch. 4.CR - Prob. 75CR Ch. 4.CR - Prob. 76CR Ch. 4.CR - Prob. 77CR Ch. 4.CR - Prob. 78CR Ch. 4.CR - Prob. 79CR Ch. 4.CR - Prob. 80CR Ch. 4.CR - Prob. 81CR Ch. 4.CR - Prob. 82CR Ch. 4.CR - Prob. 83CR Ch. 4.CR - Prob. 84CR Ch. 4.CR - Prob. 85CR Ch. 4.CR - Prob. 86CR Ch. 4.CR - Prob. 87CR Ch. 4.CR - Prob. 88CR Ch. 4.CR - Prob. 89CR Ch. 4.CR - Exponential Growth Suppose a population is growing...Ch. 4.CR - Logistic Growth Suppose a population can be...Ch. 4.CR - Fish The length of the monkeyface prickleback, a...Ch. 4.CR - Prob. 93CR Ch. 4.CR - Prob. 94CR Ch. 4.CR - Prob. 95CR Ch. 4.CR - Prob. 96CR Ch. 4.CR - Prob. 97CR Ch. 4.CR - Prob. 98CR Ch. 4.CR - Prob. 99CR Ch. 4.CR - Prob. 100CR Ch. 4.CR - Prob. 101CR Ch. 4.EA - Suppose that a particular plot of land can sustain...Ch. 4.EA - Prob. 2EA

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