First Course in Differential Equations (Instructor's)
11th Edition
ISBN: 9781305965775
Author: ZILL
Publisher: CENGAGE L
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Chapter A, Problem 47E
To determine
The derivative of the function
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#18) Find the indicated derivative for each function
For f(x) and g(x) given in Problems 35–38, find
(a) (f + g)(x)
(b) (f – g)(x)
(c) (f'g)(x)
(d) (f/g)(x)
35. f(x) = 3x g(x) = x'
36. f(x) = Vx g(x) = 1/x
37. f(x) = V2x g(x) = x²
38. f(x) = (x – 1)? g(x) = 1 – 2x
Click to
%3D
For f(x) and g(x) given in Problems 39–42, find
(a) (fº g)(x)
(b) (g •f)(x)
(c) ƒ(f(x))
(d) f(x) = (f·f)(x)
39. f(x) = (x – 1)³ g(x) = 1 – 2x
40. f(x) = 3x g(x) = x' – 1
41. f(x) = 2Vx g(x) = x* + 5
%3D
%3D
1
42. f(x) = g(x) = 4x + 1
4. Find all derivatives of f (x) = x*, where k is some unknown natural
number.
Chapter A Solutions
First Course in Differential Equations (Instructor's)
Ch. A - In Problems 1 and 2 evaluate the given quantity....Ch. A - Prob. 2ECh. A - Prob. 3ECh. A - Prob. 4ECh. A - Prob. 5ECh. A - Prob. 6ECh. A - Prob. 7ECh. A - Prob. 8ECh. A - Prob. 9ECh. A - Prob. 10E
Ch. A - Prob. 11ECh. A - Prob. 12ECh. A - Prob. 13ECh. A - Prob. 14ECh. A - Prob. 15ECh. A - Prob. 16ECh. A - Prob. 17ECh. A - Prob. 18ECh. A - Prob. 19ECh. A - Prob. 20ECh. A - Prob. 21ECh. A - Prob. 22ECh. A - Prob. 23ECh. A - Prob. 24ECh. A - In Problems 25 and 26 use the indicated...Ch. A - Prob. 26ECh. A - Prob. 27ECh. A - Prob. 28ECh. A - Prob. 29ECh. A - Prob. 30ECh. A - Prob. 31ECh. A - Prob. 32ECh. A - Prob. 33ECh. A - Prob. 34ECh. A - Show that the beta function is symmetric in x and...Ch. A - Prob. 36ECh. A - Prob. 37ECh. A - Prob. 38ECh. A - Prob. 39ECh. A - Prob. 40ECh. A - Prob. 41ECh. A - Prob. 42ECh. A - Prob. 43ECh. A - Prob. 44ECh. A - Prob. 45ECh. A - Prob. 46ECh. A - Prob. 47ECh. A - Prob. 48ECh. A - Prob. 49ECh. A - Prob. 50ECh. A - Prob. 51ECh. A - Prob. 52ECh. A - Prob. 53ECh. A - Prob. 54ECh. A - Prob. 55ECh. A - Prob. 56E
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- 4) By using Newton's backward formula for the derivative, find f (0-9) o f" (0-9) 6 1 (0-8) £ (0.8) N 0.2 0.4 f 1 3.2 0-12 +1 2arrow_forward1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x – 1)(x+1)] c. y = In- X -1arrow_forward(a) Use Definition 5.2.1(Differentiability). to produce the proper formula for the derivative of h(x) = 1/x.arrow_forward
- 3 1. Determine the derivative to y = x + y + 2xyarrow_forwardLet f(x), g(x) and h(x) be the functions from Problem A.1. Find the derivative of the following function with respect to x: derivative(x) = f(x) . g(x) + f(x) . h(x) - g(x) . h(x)arrow_forwardFind the derivative f0m(x) of the following function with respect to x:fm(x) = Xmn=1nx· xn!2arrow_forward
- O B. 7(In 100)* -1 Find the derivative of y with respect to the independent variable. y = ( In 100)" O A. 100 In 100)*-1 OC. (100)" In O D. 1( In 10)*- I-1arrow_forward1. Suppose the function V represents the number of people vaccinated for COVID-19 in Kalamazoo country. (a) What can you conclude about the first and second derivatives of V from the statement "The number of people vaccinated is increasing faster and faster"? For your conclusion, choose from among: positive, negative, zero, or other. If other, please explain. i. V'(t) is ii. V"(t) is (b) What can you conclude about the first and second derivatives of V from the statement "The number of people vaccinated is close to reaching an all time high"? For your conclusion, choose from among: positive, negative, zero, or other. If other, please explain. i. V'(t) is ii. V"(t) isarrow_forwardProblem 2: Assume thatf and g are differentiable functions. Find the derivative of y = f(x)[g(x)]¬' using the Product Rule and Chain Rule. Explain how this calculation relates to the Quotient Rule.arrow_forward
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