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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 8)^{9})

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

(3)^{x}

\frac{\partial}{\partial x} (5 y e^{x} - ln (z))

\int \frac{1}{x ^{4}} - \frac{1}{4 x} - 4 d x

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