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Popular >

derivative of x/(2x^2+1)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

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

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

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

Graph

Popular Examples

integral of (7+x^5)^65x^4

\int (7 + x^{5})^{6} 5 x^{4} d x

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\frac{d}{d x} (cos (\frac{1}{2} x))

y^{''}-16y^'+64y=8t^6e^{8t}

y^{^{''}} - 16 y^{^{'}} + 64 y = 8 t^{6} e^{8 t}

derivative of sqrt(x^2+17)

\frac{d}{d x} (x^{2} + 17)

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\frac{d}{d x} (2 ln (x) + 3)

Frequently Asked Questions (FAQ)

What is the derivative of x/(2x^2+1) ?
The derivative of x/(2x^2+1) is (-2x^2+1)/((2x^2+1)^2)
What is the first derivative of x/(2x^2+1) ?
The first derivative of x/(2x^2+1) is (-2x^2+1)/((2x^2+1)^2)