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Popular >

derivative of x/(x^2+4)

Solution

derivative of

\frac{x}{x ^{2} + 4}

Solution

\frac{- x ^{2} + 4}{( x ^{2} + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 4 ) - \frac{d}{d x} ( x ^{2} + 4 ) x}{( x ^{2} + 4 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 4) = 2 x

= \frac{1 \cdot ( x ^{2} + 4 ) - 2 xx}{( x ^{2} + 4 ) ^{2}}

1 \cdot (x^{2} + 4) - 2 xx = - x^{2} + 4

= \frac{- x ^{2} + 4}{( x ^{2} + 4 ) ^{2}}

Popular Examples

derivative of sqrt(x\sqrt{x^2+1)}derivative of

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of x/(x^2+4) ?
The derivative of x/(x^2+4) is (-x^2+4)/((x^2+4)^2)
What is the first derivative of x/(x^2+4) ?
The first derivative of x/(x^2+4) is (-x^2+4)/((x^2+4)^2)