# Solve for: f(x)=(1)/(x^3)

## Expression: $f\left( x \right)=\frac{ 1 }{ {x}^{3} }$

Take the derivative of both sides

$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( \frac{ 1 }{ {x}^{3} } \right)$

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

$f '\left( x \right)=-\frac{ 3 }{ {x}^{4} }$

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