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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int (\frac{11}{x} + \frac{x}{11}) d x

y^{^{''}} - 14 y^{^{'}} + 53 y = 0

\int 20 cos (10 t + \frac{π}{6}) + 2 d t

\int \frac{cos ( 3 x )}{sin ( 3 x )} d x

f (x) = - 6 x

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