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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

\frac{1 \cdot ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) x}{( ( x ^{2} + 1 ) ^{2} ) ^{2}} : \frac{- 3 x ^{2} + 1}{( x ^{2} + 1 ) ^{3}}

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

\int \frac{12}{1 + 4 x ^{2}} d x

\frac{d}{d x} (3 x^{9.6} + 2 e^{1.3})

\int_{1}^{2} (\frac{1}{t} - i)^{2} d t

y^{^{'}} = a y - b y^{2}

\frac{d}{d x} (\frac{x ^{8}}{16})

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