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Popular >

derivative of x/(x^3-1)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (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

integral of (u+4)(2u+1)

\int (u + 4) (2 u + 1) d u

y^{''}-2y^'+2y=cos(t),y(0)=1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} + 2 y = cos (t), y (0) = 1, y^{^{'}} (0) = 0

integral of 1/(sqrt(2+x^2))

\int \frac{1}{2 + x ^{2}} d x

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\int \frac{1}{x ^{2}} e^{l n (x)} d x

derivative of (2x^3/3-8x-5)

\frac{d}{d x} (\frac{2 x ^{3}}{3} - 8 x - 5)

Frequently Asked Questions (FAQ)

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