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Popular >

derivative of f(x)= x/(x^2-5)

Solution

derivative of

f (x) = \frac{x}{x ^{2} - 5}

Solution

\frac{- x ^{2} - 5}{( x ^{2} - 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{1 \cdot ( x ^{2} - 5 ) - 2 xx}{( x ^{2} - 5 ) ^{2}}

1 \cdot (x^{2} - 5) - 2 xx = - x^{2} - 5

= \frac{- x ^{2} - 5}{( x ^{2} - 5 ) ^{2}}

Popular Examples

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

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\int \frac{( x ^{2} - 64 )}{x} d x

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x^2-5) ?
The derivative of f(x)= x/(x^2-5) is (-x^2-5)/((x^2-5)^2)
What is the first derivative of f(x)= x/(x^2-5) ?
The first derivative of f(x)= x/(x^2-5) is (-x^2-5)/((x^2-5)^2)