31642623
Description
Quiz by IWKZ Tutorium, updated more than 1 year ago
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Created by IWKZ Tutorium
over 3 years ago
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Question 1
Question
Geben Sie die Ableitung von \( x^2 \ln(\frac{4x^2}{9}) \)
Answer
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\[ f'(x) = 2x( \ln(\frac{4x^2}{9}) + 1 ) \]
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\[ f'(x) = 2x \ln( \frac{4x^2}{9} ) + \frac{9}{4x^2} \]
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\[ f'(x) = \ln( \frac{4x^2}{9} ) + 1 \]
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\[ f'(x) = x( \ln(\frac{4x^2}{9}) + 1 ) \]
Question 2
Question
Geben Sie die Ableitung von \( (x-4)e^{x^2 + 2x + 1} \)
Answer
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\[ f'(x) = (2x^2 - 6x - 7)e^{x^2 + 2x + 1} \]
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\[ f'(x) = e^{x^2 + 2x + 1} \]
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\[ f'(x) = (2x + 2)e^{x^2 + 2x + 1} \]
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\[ f'(x) = (2x^2 - 6x - 8)e^{x^2 + 2x + 1} \]
Question 3
Question
Geben Sie die Ableitung von \( \frac{e^{x^2} (x-2)^2}{2x^2} \)
Answer
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\[ f'(x) = \frac{e^{x^2} (x-2) [x^3 - 2x^2 + 2]}{x^3} \]
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\[ f'(x) = \frac{2e^{x^2}}{3x^2} \]
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\[ f'(x) = \frac{4xe^{x^2}}{3x^2} \]
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\[ f'(x) = \frac{2e^{x^2} (x-2)}{x^3} \]
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