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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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\int_{0}^{3} x^{2} e^{- x} d x

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\int (lo g_{e} (x))^{2} d x

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\int (\frac{4}{x ^{2}} + 2 - \frac{1}{8 x ^{3}}) d x

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)