(\partial)/(\partial x)(1/(sqrt(1+x^2)))

解答

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

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

\frac{d}{d x} (\frac{1}{16} e^{2 x^{2}})

a re a y = 2 x + 2, y = x^{2} + 2, x = - 1, x = 3

x \to - π lim (\frac{sin ( x )}{x})

\int 2 t + 1 d t

d er i v a t i v e y = ln (1 - x^{2})