Calculus For The Life Sciences 2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
P Prerequisite Skills Diagnostic Test R Algebra Reference 1 Functions 2 Exponential, Logarithmic, And Trigonometric Functions 3 The Derivative 4 Calculating The Derivative 5 Graphs And The Derivative 6 Applications Of The Derivative 7 Integration 8 Further Techniques And Applications Of Integration 9 Multivariable Calculus 10 Matrices 11 Differential Equations 12 Probability 13 Probability And Calculus 14 Discrete Dynamical Systems Chapter4: Calculating The Derivative
4.1 Techniques For Finding Derivatives 4.2 Derivatives Of Products And Quotients 4.3 The Chain Rule 4.4 Derivatives Of Exponential Functions 4.5 Derivatives Of Logarithmic Functions 4.6 Derivatives Of Trigonometric Functions 4.CR Chapter 4 Review 4.EA Extended Application Managing Renewable Resources Section4.4: Derivatives Of Exponential Functions
Problem 1YT: YOUR TURN 1 Find dy/dx for a. y=43x, b. y=e7x3+5 Problem 2YT Problem 3YT Problem 4YT: YOUR TURN 4 The quantity in grams of a radioactive substance present after t years is... Problem 1E Problem 2E Problem 3E: Find derivatives of the functions defined as follows. y=-8e3x Problem 4E Problem 5E Problem 6E: Find derivatives of the functions defined as follows. y=-4e-0.3x Problem 7E: Find derivatives of the functions defined as follows. y=ex2 Problem 8E: Find derivatives of the functions defined as follows. y=e-x2 Problem 9E: Find derivatives of the functions defined as follows. y=3e2x2 Problem 10E Problem 11E Problem 12E: Find derivatives of the functions defined as follows. y=-3e3x2+5 Problem 13E Problem 14E Problem 15E: Find derivatives of the functions defined as follows. y=x+32e4x Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E: Find derivatives of the functions defined as follows. p=10,0009+4e-0.2t Problem 22E: Find derivatives of the functions defined as follows. p=50012+5e-0.5t Problem 23E: Find derivatives of the functions defined as follows. fz=2z+e-z22 Problem 24E: Find derivatives of the functions defined as follows. ft=et2+5t3 Problem 25E Problem 26E: Find derivatives of the functions defined as follows. y=4-5x+2 Problem 27E: Find derivatives of the functions defined as follows. y=34x2+2 Problem 28E Problem 29E Problem 30E: Find derivatives of the functions defined as follows. s=52t-2 Problem 31E Problem 32E: Find derivatives of the functions defined as follows. y=t2e2tt+e3t Problem 33E Problem 34E: Find derivatives of the functions defined as follows. fx=ex2/x3+2 Problem 35E Problem 36E Problem 37E: Use graphical differentiation to verify that ddxex=ex. Problem 38E Problem 40E: Population Growth In section 2.1, Exercise 37, the growth in world population in millions was... Problem 41E: Minority Population In Section 2.1, Exercise 39, we saw that the projected Hispanic population in... Problem 42E: Insect Growth The growth of a population of rare South American beetles is given by the logistic... Problem 43E Problem 44E: Whooping Cranes Based on data from the U.S. Fish and Wildlife Service, the population of whooping... Problem 45E Problem 46E Problem 47E: Mortality The percentage of people of any particular age group that will die in a given year may be... Problem 48E: Breast Cancer It has been observed that the following formula accurately models the relationship... Problem 49E: Arctic Foxes The age-weight relationship of female Arctic foxes caught in Svalbard, Norway, can be... Problem 50E Problem 51E: Ayrshire Dairy Cattle The researchers from the previous exercise also developed a function that can... Problem 52E: Cutlassfish The cutlassfish is one of the most important resource of the commercial marine fishing... Problem 53E Problem 54E: Dialysis One measure of whether a dialysis patient has been adequately dialyzed is by the urea... Problem 55E: Medical Literature It has been observed that there has been an increase in proportion of medical... Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E: Radioactive Iron Researchers found that the fraction of radioactive iron in one patients blood... Problem 62E Problem 63E Problem 64E Problem 65E: Habit Strength According to work by the psychologist C. L. Hull, the strength of a habit is a... Problem 66E Problem 67E: Electricity In a series resistance-capacitance DC circuit, the instantaneous charge Q on the... Problem 68E Problem 69E Problem 18E
Differentiate the following functions requiring use of Chain Rule. (Any value that is not the function variable should be considered a constant)
Transcribed Image Text: 5. f(x) = sec [(x³ + 3) (√√x + x)]
6. y = 4 cos 3x
1
7. f(x) =
3+ sin² x
Transcribed Image Text: 8. y = (cscx +
(csc x + 2) 5 + x² + x
9. y = tan +
tan(70)
10. 9(x) = (√√x + √x)
(√ + √x) (x² – 1)7
-
3
-
11. f(x) =
X 3
x+1
12. A(t) = cos(wt + 0); Also find
13. f(x) = sin [cos (x² + x)]
dA
dt
t=0
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
![5. f(x) = sec [(x³ + 3) (√√x + x)]
6. y = 4 cos 3x
1
7. f(x) =
3+ sin² x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5804317c-00e5-4792-adfc-03b254ca09f6%2F7f010a03-63df-479d-8d06-cfb26f01a36b%2Fl4t273e_processed.png&w=3840&q=75)
![8. y = (cscx +
(csc x + 2) 5 + x² + x
9. y = tan +
tan(70)
10. 9(x) = (√√x + √x)
(√ + √x) (x² – 1)7
-
3
-
11. f(x) =
X 3
x+1
12. A(t) = cos(wt + 0); Also find
13. f(x) = sin [cos (x² + x)]
dA
dt
t=0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5804317c-00e5-4792-adfc-03b254ca09f6%2F7f010a03-63df-479d-8d06-cfb26f01a36b%2Fe1zphyf_processed.png&w=3840&q=75)
