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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{e ^{x}}{e ^{x} + e ^{y}})

\frac{\partial}{\partial y} (x y arcsin (yz))

\frac{d}{d x} (e^{- (c o s (x) + s i n (y))})

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{5 + 4 x})

\int (5 x) d x

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