Differentiating this problem $\frac{2{t}^{3/2}}{\mathrm{ln}(2{t}^{3/2}+1)}$

How does one differentiate the function

$$y(t)=\frac{2{t}^{3/2}}{\mathrm{ln}(2{t}^{3/2}+1)}.$$

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?

How does one differentiate the function

$$y(t)=\frac{2{t}^{3/2}}{\mathrm{ln}(2{t}^{3/2}+1)}.$$

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?