TOPIC 2: Derivatives of Logarithmic Functions (ba Basic Rules: (In x)': a) f(x)=- +2 In(x) 2 X . where In x = log, x Q.#5 Please find the derivatives of the following functions. b) g(t) = 2log (1) fix = 1 (In (²) +2) P'LD) = 1 (INC) + (2 { x = = = = = +0 f'(x) = ax (log, x) = 11 x In a xln a Final Answer 1 f'(x) = ax Final Answer
TOPIC 2: Derivatives of Logarithmic Functions (ba Basic Rules: (In x)': a) f(x)=- +2 In(x) 2 X . where In x = log, x Q.#5 Please find the derivatives of the following functions. b) g(t) = 2log (1) fix = 1 (In (²) +2) P'LD) = 1 (INC) + (2 { x = = = = = +0 f'(x) = ax (log, x) = 11 x In a xln a Final Answer 1 f'(x) = ax Final Answer
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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![TOPIC 2: Derivatives of Logarithmic Functions (basic rules, combos with other rules, etc.)
Basic Rules: (In x) = - , where In x = log, x
Q.#5 Please find the derivatives of the following functions.
In(x)
2
fix) = 1 (Inc)
f'(x) =
a) f(x) =
+2
b) g(t) = 2log s(t)
(INC) + (2)
f/1x) = = = = = = = + +0
f'(x) = 2x
9'(t) = 3 (2 logs (1)
9' (t) = 2 · 3 (1095 (t))
.
9 '(t) = 2.
I
In (5)+
2
In (5) +
9' (t) =
c) f(x)=xlnx-x
f'(x) = x (x-In (x) - x)
f'ci) = x (x. In (x) - — (0)
-
dx
dx
f'(x) = In (x) + x² = -1
X
f'(x)= In (x)
(log, x)
11
x In a
1
x ln a
Final Answer
f'(x) = ax
Final Answer
9(A) =
Ə
In/5)+
Final Answer
f'(x) = In (x)
Page 8 of 16](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbed15dc4-f7d5-4c59-88ec-c5b05b5850af%2F689c5f9e-e833-4b97-bb6a-cd546812f559%2F0dkrxwe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:TOPIC 2: Derivatives of Logarithmic Functions (basic rules, combos with other rules, etc.)
Basic Rules: (In x) = - , where In x = log, x
Q.#5 Please find the derivatives of the following functions.
In(x)
2
fix) = 1 (Inc)
f'(x) =
a) f(x) =
+2
b) g(t) = 2log s(t)
(INC) + (2)
f/1x) = = = = = = = + +0
f'(x) = 2x
9'(t) = 3 (2 logs (1)
9' (t) = 2 · 3 (1095 (t))
.
9 '(t) = 2.
I
In (5)+
2
In (5) +
9' (t) =
c) f(x)=xlnx-x
f'(x) = x (x-In (x) - x)
f'ci) = x (x. In (x) - — (0)
-
dx
dx
f'(x) = In (x) + x² = -1
X
f'(x)= In (x)
(log, x)
11
x In a
1
x ln a
Final Answer
f'(x) = ax
Final Answer
9(A) =
Ə
In/5)+
Final Answer
f'(x) = In (x)
Page 8 of 16
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