derivative of 7-4/(x-8+(2x)/(3x+1))

解答

\frac{d}{d x} (7 - \frac{4}{x - 8} + \frac{2 x}{3 x + 1})

\frac{38 x ^{2} - 8 x + 132}{( x - 8 ) ^{2} ( 3 x + 1 ) ^{2}}

求解步骤

\frac{d}{d x} (7 - \frac{4}{x - 8} + \frac{2 x}{3 x + 1})

化简

7 - \frac{4}{x - 8} + \frac{2 x}{3 x + 1} : \frac{2 x ^{2} - 28 x - 4}{( x - 8 ) ( 3 x + 1 )} + 7

= \frac{d}{d x} (\frac{2 x ^{2} - 28 x - 4}{( x - 8 ) ( 3 x + 1 )} + 7)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{2 x ^{2} - 28 x - 4}{( x - 8 ) ( 3 x + 1 )}) + \frac{d}{d x} (7)

\frac{d}{d x} (\frac{2 x ^{2} - 28 x - 4}{( x - 8 ) ( 3 x + 1 )}) = \frac{38 x ^{2} - 8 x + 132}{( x - 8 ) ^{2} ( 3 x + 1 ) ^{2}}

\frac{d}{d x} (7) = 0

= \frac{38 x ^{2} - 8 x + 132}{( x - 8 ) ^{2} ( 3 x + 1 ) ^{2}} + 0

化简

= \frac{38 x ^{2} - 8 x + 132}{( x - 8 ) ^{2} ( 3 x + 1 ) ^{2}}

\int \frac{31}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\int tan (6 x + 1) d x

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

d er i v a t i v e arcsin (\frac{x}{7})

d er i v a t i v e y = 4^{- x} sin (x)