Differentiate ((3x^3)/( x)) with respect to x.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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 $x$:
$$ \frac{d}{dx}(\ln(3)) = 0 $$
$$ \frac{d}{dx}(3\ln(x)) =
