What is the derivative of ((x^2+2/(x^3-1))^3) ?

The derivative of ((x^2+2/(x^3-1))^3) is (3(x^2+2)^2(-x^4-6x^2-2x))/((x^3-1)^4)

What is the first derivative of ((x^2+2/(x^3-1))^3) ?

The first derivative of ((x^2+2/(x^3-1))^3) is (3(x^2+2)^2(-x^4-6x^2-2x))/((x^3-1)^4)

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\frac{d}{d x} ((\frac{x ^{2} + 2}{x ^{3} - 1})^{3})

\frac{3 ( x ^{2} + 2 ) ^{2} ( - x ^{4} - 6 x ^{2} - 2 x )}{( x ^{3} - 1 ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{x ^{2} + 2}{x ^{3} - 1})^{3})

Apply the chain rule:

3 (\frac{x ^{2} + 2}{x ^{3} - 1})^{2} \frac{d}{d x} (\frac{x ^{2} + 2}{x ^{3} - 1})

= 3 (\frac{x ^{2} + 2}{x ^{3} - 1})^{2} \frac{d}{d x} (\frac{x ^{2} + 2}{x ^{3} - 1})

\frac{d}{d x} (\frac{x ^{2} + 2}{x ^{3} - 1}) = \frac{- x ^{4} - 6 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}}

= 3 (\frac{x ^{2} + 2}{x ^{3} - 1})^{2} \frac{- x ^{4} - 6 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}}

Simplify

3 (\frac{x ^{2} + 2}{x ^{3} - 1})^{2} \frac{- x ^{4} - 6 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}} : \frac{3 ( x ^{2} + 2 ) ^{2} ( - x ^{4} - 6 x ^{2} - 2 x )}{( x ^{3} - 1 ) ^{4}}

= \frac{3 ( x ^{2} + 2 ) ^{2} ( - x ^{4} - 6 x ^{2} - 2 x )}{( x ^{3} - 1 ) ^{4}}

What is the derivative of ((x^2+2/(x^3-1))^3) ?
The derivative of ((x^2+2/(x^3-1))^3) is (3(x^2+2)^2(-x^4-6x^2-2x))/((x^3-1)^4)
What is the first derivative of ((x^2+2/(x^3-1))^3) ?
The first derivative of ((x^2+2/(x^3-1))^3) is (3(x^2+2)^2(-x^4-6x^2-2x))/((x^3-1)^4)