derivative of 1/(sqrt(x+sin(x)))

解答

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

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

\frac{d}{d x} (x + sin (x)) = 1 + cos (x)

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

化简

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

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

\frac{d y}{d x} = \frac{4 e ^{4 x}}{e ^{y}}

\int 2 e^{- s t} d t

in v erse l a pl a ce \frac{( s - 1 )}{s ^{2} + 2 s + 2}

x \to \infty lim (3 - f (x))

t an g e n t 8 x^{3} - 36 x^{2} - 96