12x+1 C) (2x+ 1)2 7) If y= then *+2. dy 12x -1 D) (2x+ 1)2 2x12x•5 A) (x+2)2 7 E) (2x+ 1)2 2x B) 22x C) (x+ 2)2 3) If x2 - 2xy + y3 = 10, then dx 2y-2x A) 3y2 . 2x D) (x• 2)2 2x(2x+ 3 E) (*+ 2)2 2y+ 2x B) 3y2 • 2x 2y- 2x C) 3,2-2x 8) For differentiable functions f and g, the table below shows various values for f(x) and g(x) as well as their derivatives, f'(x) and g'(x). 2y+2x D) 3y2 - 2x 2y- 2x+2 E) 3y2 f(x) f'(x) g(x) g') 3 5 1 2 4 2 -1 1 -3 4) If f(x) = csc x tan x, then f'(x) = 1 A) sin x cos x If H(x) = g[f(x)], then H'(1) = A) O B) sec x tan x B) -15 C) -3 D) 10 C) -csc x cot x 1 D) sin x E) -sec x tan x E) 20
12x+1 C) (2x+ 1)2 7) If y= then *+2. dy 12x -1 D) (2x+ 1)2 2x12x•5 A) (x+2)2 7 E) (2x+ 1)2 2x B) 22x C) (x+ 2)2 3) If x2 - 2xy + y3 = 10, then dx 2y-2x A) 3y2 . 2x D) (x• 2)2 2x(2x+ 3 E) (*+ 2)2 2y+ 2x B) 3y2 • 2x 2y- 2x C) 3,2-2x 8) For differentiable functions f and g, the table below shows various values for f(x) and g(x) as well as their derivatives, f'(x) and g'(x). 2y+2x D) 3y2 - 2x 2y- 2x+2 E) 3y2 f(x) f'(x) g(x) g') 3 5 1 2 4 2 -1 1 -3 4) If f(x) = csc x tan x, then f'(x) = 1 A) sin x cos x If H(x) = g[f(x)], then H'(1) = A) O B) sec x tan x B) -15 C) -3 D) 10 C) -csc x cot x 1 D) sin x E) -sec x tan x E) 20
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.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 37E: Use graphical differentiation to verify that ddxex=ex.
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Topic Video
Question
Questions 6 and 8
![12x+1
e2x
If y=
dy
then
dx
7)
(2x+ 1)2
*+ 2 '
12x -1
D)
(2x+ 1)2
2x(2x+5
A)
(x+ 2)2
7
E)
(2x + 1)2
B)
C)
(x+ 2)2
3)
dy
If x2 - 2xy + y3 = 10, then
2x(x+ 1)
D)
(x+ 2)2
e2x(2x+ 3
E)
(x+ 2)2
A)
2y-2x
3y2 + 2x
2y+ 2x
B)
3y2 + 2x
2y-2x
C)
For differentiable functions f and g, the table
8)
below shows various values for f(x) and g(x) as well
as their derivatives, f'(x) and g'(x).
3y2 - 2x
2y+2x
D)
3 y2 - 2x
2y- 2x+ 2
3y2
E)
f(x) f'(x)| g(x) g'x)
1
3
4
2
-1
1
-3
4)
If f(x) = csc x tan x, then f'(x) =
1
A)
sin? x cos x
If H(x) = g[f(x)], then H' (1) =
A) O
B) -15
C) -3
D) 10
B) sec x tan x
C) -csc x cot x
1
D)
sin x
E) -sec x tan x
E) 20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F694ca289-8529-4823-b99c-63315efae91e%2F71980e38-af5f-43ca-b883-15305a585249%2F43bllh6_processed.png&w=3840&q=75)
Transcribed Image Text:12x+1
e2x
If y=
dy
then
dx
7)
(2x+ 1)2
*+ 2 '
12x -1
D)
(2x+ 1)2
2x(2x+5
A)
(x+ 2)2
7
E)
(2x + 1)2
B)
C)
(x+ 2)2
3)
dy
If x2 - 2xy + y3 = 10, then
2x(x+ 1)
D)
(x+ 2)2
e2x(2x+ 3
E)
(x+ 2)2
A)
2y-2x
3y2 + 2x
2y+ 2x
B)
3y2 + 2x
2y-2x
C)
For differentiable functions f and g, the table
8)
below shows various values for f(x) and g(x) as well
as their derivatives, f'(x) and g'(x).
3y2 - 2x
2y+2x
D)
3 y2 - 2x
2y- 2x+ 2
3y2
E)
f(x) f'(x)| g(x) g'x)
1
3
4
2
-1
1
-3
4)
If f(x) = csc x tan x, then f'(x) =
1
A)
sin? x cos x
If H(x) = g[f(x)], then H' (1) =
A) O
B) -15
C) -3
D) 10
B) sec x tan x
C) -csc x cot x
1
D)
sin x
E) -sec x tan x
E) 20
Transcribed Image Text:1)
If f(x) = - 2x³, then f' (8) =
5)
If f(x) = sin? (2x), then f'
A)
3
A)
2
B) 2/3
C) 2
D)
E) 4
B)
C)
D)
E)
If f(x) = tan (2x2), then f'(/n) =
A) Vn
B) 4/T
C) 1
D) 2/
E) о
6)
%3D
3x - 2
2)
If f(x) =
then f'(x) =
2x+1
A) 2
-7
В)
(2x+ 1)2
e2x
If y=
12x+1
C)
(2x+ 1)2
12x -1
D)
(2x+ 1)2
7)
dy
then
dx
*+2 :
2x(2x+5
A)
(x+ 2)2
E)
(2x+ 1)2
B)
C)
(x+ 2)2
3)
dy
If x2 - 2xy + y3 = 10, then
e2x(x+ 1)
%3D
dx
2y-2x
A)
3y2 + 2x
D)
(x+ 2)2
e2 x(2x+ 3
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