Question
Let
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Select each of the true statements from the following:
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For the outside function is and the argument is
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For the outside function is and the argument is
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For the outside function is and the argument is
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All of the above statements are false.
Solution
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False. The composition of and is
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True. For the outside function is and the argument (or inside function) is . The composition of and is
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True. For the outside function is and the argument (or inside function) is . The composition of and is
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False. What function(s) could have derivative ? Since the derivative of with respect to is you can check that the derivative of is an answer to this question.
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False. What function(s) could have derivative ? This question is beyond the scope of this course but the process used to find an answer involves the product rule. Incorrect use of the power rule may be the reason someone would think
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False. The chain rule states where the outside function is and the argument (or inside function) is . Since (not ) and
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False.