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Popular >

(x/(x^3-1))^'

Solution

(\frac{x}{x ^{3} - 1})^{^{'}}

Solution

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

Solution steps

(\frac{x}{x ^{3} - 1})^{'}

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

x^{'} = 1

(x^{3} - 1)^{'} = 3 x^{2}

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

1 \cdot (x^{3} - 1) - 3 x^{2} x = - 2 x^{3} - 1

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

Graph

Popular Examples

derivative of (4-4x/(3x^{2/3)})

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derivative of e^{2x}+1 derivative of

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\int_{0}^{\infty} \frac{e ^{x}}{1 + e ^{x}} d x

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f (x) = 4 x^{2} + 3 x + 6, (- 4, 58)

derivative of cos(axa)

\frac{d}{d x} (cos (a x) a)

Frequently Asked Questions (FAQ)

What is the (x/(x^3-1))^' ?
The (x/(x^3-1))^' is (-2x^3-1)/((x^3-1)^2)
What is the first (x/(x^3-1))^' ?
The first (x/(x^3-1))^' is (-2x^3-1)/((x^3-1)^2)