$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( \frac{ 1 }{ {x}^{3} } \right)$
Use differentiation rule $\frac{ \mathrm{d} }{ \mathrm{d}x} \left( \frac{ 1 }{ f } \right)=-\frac{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( f \right) }{ {f}^{2} }$$f '\left( x \right)=-\frac{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{3} \right) }{ {\left( {x}^{3} \right)}^{2} }$
Use $\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{n} \right)=n \times {x}^{n-1}$ to find derivative$f '\left( x \right)=-\frac{ 3{x}^{2} }{ {\left( {x}^{3} \right)}^{2} }$
Simplify the expression$f '\left( x \right)=-\frac{ 3 }{ {x}^{4} }$