Differentiate ((3x³)/( x)) with respect to x.

Step 1: Differentiate $\ln\left(\frac{3x^3}{\sin x}\right)$ with respect to $x$.
First, simplify the expression using logarithm properties:

$$\ln\left(\frac{3x^3}{\sin x}\right) = \ln(3x^3) - \ln(\sin x) = \ln(3) + \ln(x^3) - \ln(\sin x) = \ln(3) + 3\ln(x) - \ln(\sin x)$$

Now, differentiate each term with respect to $x$:

$$\frac{d}{dx}(\ln(3)) = 0$$ $$$$