derivative of (-2/(x-5)-3)

解答

\frac{d}{d x} (\frac{- 2}{x - 5} - 3)

\frac{2}{( x - 5 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{- 2}{x - 5} - 3)

化简

\frac{- 2}{x - 5} - 3 : - \frac{2}{x - 5} - 3

= \frac{d}{d x} (- \frac{2}{x - 5} - 3)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (\frac{2}{x - 5}) - \frac{d}{d x} (3)

\frac{d}{d x} (\frac{2}{x - 5}) = - \frac{2}{( x - 5 ) ^{2}}

\frac{d}{d x} (3) = 0

= - (- \frac{2}{( x - 5 ) ^{2}}) - 0

化简

= \frac{2}{( x - 5 ) ^{2}}

\frac{d}{d x} (\frac{1}{12 x ^{2}})

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

\int \frac{cos ( t )}{sin ( t )} d t

x^{2} \frac{d y}{d x} + x (x + 2) = e^{x}

n \to 0 lim (\frac{( ( 3 ) ^{n} - 1 )}{n})