What is the derivative of (sqrt(x)/(1+x^2)) ?

The derivative of (sqrt(x)/(1+x^2)) is (1-3x^2)/(2sqrt(x)(1+x^2)^2)

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

The first derivative of (sqrt(x)/(1+x^2)) is (1-3x^2)/(2sqrt(x)(1+x^2)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

What is the derivative of (sqrt(x)/(1+x^2)) ?
The derivative of (sqrt(x)/(1+x^2)) is (1-3x^2)/(2sqrt(x)(1+x^2)^2)
What is the first derivative of (sqrt(x)/(1+x^2)) ?
The first derivative of (sqrt(x)/(1+x^2)) is (1-3x^2)/(2sqrt(x)(1+x^2)^2)