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Popular >

derivative of x/(x^2-8)

Solution

derivative of

\frac{x}{x ^{2} - 8}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Popular Examples

integral of x-(1/2)^x

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

limit as x approaches infinity of 4^x-1

x \to \infty lim (4^{x} - 1)

limit as x approaches 3 of ((x^2-9))/(2x-6)

x \to 3 lim (\frac{( x ^{2} - 9 )}{2 x - 6})

limit as x approaches infinity of (2^x)/(3^{x-1)}

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

integral of sqrt(2-x)

\int 2 - x d x

Frequently Asked Questions (FAQ)

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