What is the derivative of ((x^3/(x^4-2x))^3) ?

The derivative of ((x^3/(x^4-2x))^3) is -(3x^5(x^3+4))/((x^3-2)^4)

What is the first derivative of ((x^3/(x^4-2x))^3) ?

The first derivative of ((x^3/(x^4-2x))^3) is -(3x^5(x^3+4))/((x^3-2)^4)

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\frac{d}{d x} ((\frac{x ^{3}}{x ^{4} - 2 x})^{3})

- \frac{3 x ^{5} ( x ^{3} + 4 )}{( x ^{3} - 2 ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{x ^{3}}{x ^{4} - 2 x})^{3})

Apply the chain rule:

3 (\frac{x ^{3}}{x ^{4} - 2 x})^{2} \frac{d}{d x} (\frac{x ^{3}}{x ^{4} - 2 x})

= 3 (\frac{x ^{3}}{x ^{4} - 2 x})^{2} \frac{d}{d x} (\frac{x ^{3}}{x ^{4} - 2 x})

\frac{d}{d x} (\frac{x ^{3}}{x ^{4} - 2 x}) = - \frac{x ( x ^{3} + 4 )}{( x ^{3} - 2 ) ^{2}}

= 3 (\frac{x ^{3}}{x ^{4} - 2 x})^{2} (- \frac{x ( x ^{3} + 4 )}{( x ^{3} - 2 ) ^{2}})

Simplify

3 (\frac{x ^{3}}{x ^{4} - 2 x})^{2} (- \frac{x ( x ^{3} + 4 )}{( x ^{3} - 2 ) ^{2}}) : - \frac{3 x ^{5} ( x ^{3} + 4 )}{( x ^{3} - 2 ) ^{4}}

= - \frac{3 x ^{5} ( x ^{3} + 4 )}{( x ^{3} - 2 ) ^{4}}

What is the derivative of ((x^3/(x^4-2x))^3) ?
The derivative of ((x^3/(x^4-2x))^3) is -(3x^5(x^3+4))/((x^3-2)^4)
What is the first derivative of ((x^3/(x^4-2x))^3) ?
The first derivative of ((x^3/(x^4-2x))^3) is -(3x^5(x^3+4))/((x^3-2)^4)