Differentiating this problem (2t^(3/2))/(ln(2t^(3/2)+1))

mriteyl 2022-09-07 Answered
Differentiating this problem 2 t 3 / 2 ln ( 2 t 3 / 2 + 1 )
How does one differentiate the function
y ( t ) = 2 t 3 / 2 ln ( 2 t 3 / 2 + 1 ) .
How do I start/process solving this? Do i take the ln of both side? If so I get the log of the top - the log of the bottom. which is the log of a log? If I do the quotient rule right away, i get the log expression in the bottom squared. Help please?
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Answers (2)

barquegese2
Answered 2022-09-08 Author has 11 answers
Getting the square of the logarithm in the denominator is a fact. You have tools for differentiating, so apply them
which you can simplify if you want by distributing out the 3 t 1 / 2 , but that is in the eye of the beholder.
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eukrasicx
Answered 2022-09-09 Author has 3 answers
In this case the quotient rule is probably the best option. The symmetry of the 2 t 2 / 3 in the top and bottom makes me suspect that some things might end up canceling out.
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