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Popular >

derivative of x/(x^2+2)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Popular Examples

derivative of (e^{2x}-e^x+e^{-3x}/(e^x))

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

(\partial)/(\partial x)(2x)

\frac{\partial}{\partial x} (2 x)

integral of 1/(x^2+1)

\int \frac{1}{x ^{2} + 1} d x

(\partial)/(\partial x)(zsin(x))

\frac{\partial}{\partial x} (z sin (x))

derivative of ln(4x^2)

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

Frequently Asked Questions (FAQ)

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