Product rule
\[{d \over dx}(a\cdot b) = \dot{a}\cdot b + a \cdot \dot{b}\] \[a = \csc(3x)\] \[b = x^{-3}\] \[\dot a = -3\csc (x) \cdot \cot (x)\] \[\dot b = -3 \cdot x^{-4}\] \[(-3\csc (3x) \cdot \cot (3x)) \cdot (x^{-3}) + (\csc(3x)) \cdot (-3 \cdot x^{-4})\] \[-3 {\csc (3x) \cdot \cot (3x) \over x^3} + -3 {csc(3x) \over x^4}\] \[-3 \csc (3x) \cdot ({cot (3x) \over x^3} + {1 \over x^4})\] \[-3 \csc (3x) \cdot ({cot (3x) \over x^3}\cdot{x \over x} + {1 \over x^4})\] \[-3 \csc (3x) \cdot ({x \cdot cot (3x) + 1 \over x^4})\]