Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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
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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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