derivada de 1/(1+sqrt(x))

Solución

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

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

Pasos de solución

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

Aplicar las leyes de los exponentes:

\frac{1}{a} = a^{- 1}

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

Aplicar la regla de la cadena:

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

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

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

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

Simplificar

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

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

f (x) = arctan (ln (x))

\int \frac{32 x ^{2}}{( x - 18 ) ( x + 6 ) ^{2}} d x

2 x e^{- x^{2}} - 2 x^{3} e^{- 2 x}

\frac{d ^{3}}{d x ^{3}} (4 x + 3)

\frac{\partial}{\partial x} (2 x y z^{2} - 192)