derivative y=(2x)/(1-x^2)

Solución

derivada de

y = \frac{2 x}{1 - x ^{2}}

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

Pasos de solución

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

Sacar la constante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Aplicar la regla del cociente:

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

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

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

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

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

Simplificar

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

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

\frac{1}{8} x^{\frac{2}{3}} (9 x^{2} - 8 x - 16)

- cos (x)

- \frac{1}{x ^{2}}

f (x) = x^{2} + 1

x^{2} - 24 x - 12