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Popular >

derivative of x/(x^3-8)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{1 \cdot ( x ^{3} - 8 ) - 3 x ^{2} x}{( x ^{3} - 8 ) ^{2}}

1 \cdot (x^{3} - 8) - 3 x^{2} x = - 2 x^{3} - 8

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

Graph

Popular Examples

integral of (3x-1)/(x^2(x+1))

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

integral of ((2x-5))/((x+2)(x+3))

\int \frac{( 2 x - 5 )}{( x + 2 ) ( x + 3 )} d x

limit as x approaches 0-of x[x]cot(x)

x \to 0 - lim (x [x] cot (x))

derivative of (x^2+1/(sqrt(x^2-1)))

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

integral from 0 to 1 of 1/(x^{-2)}

\int_{0}^{1} \frac{1}{x ^{- 2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of x/(x^3-8) ?
The derivative of x/(x^3-8) is (-2x^3-8)/((x^3-8)^2)
What is the first derivative of x/(x^3-8) ?
The first derivative of x/(x^3-8) is (-2x^3-8)/((x^3-8)^2)