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

Differentiating this problem $\frac{2{t}^{3/2}}{\mathrm{ln}\left(2{t}^{3/2}+1\right)}$
How does one differentiate the function
$y\left(t\right)=\frac{2{t}^{3/2}}{\mathrm{ln}\left(2{t}^{3/2}+1\right)}.$
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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barquegese2
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
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.