derivative of 3/(((56(2x-1)^7))-1/(((24)(2x-1)^6))-1/(((40(2x-1)^5))))

解答

\frac{d}{d x} \frac{3}{( ( 56 ) ( 2 x - 1 ) ^{7} )} - \frac{1}{( ( 24 ) ( 2 x - 1 ) ^{6} )} - \frac{1}{( ( 40 ( 2 x - 1 ) ^{5} ) )}

\frac{x ^{2} - 1}{( 2 x - 1 ) ^{8}}

求解步骤

\frac{d}{d x} \frac{3}{( ( 56 ) ( 2 x - 1 ) ^{7} )} - \frac{1}{( ( 24 ) ( 2 x - 1 ) ^{6} )} - \frac{1}{( ( 40 ( 2 x - 1 ) ^{5} ) )}

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{3}{56 ( 2 x - 1 ) ^{7}}) - \frac{d}{d x} (\frac{1}{24 ( 2 x - 1 ) ^{6}}) - \frac{d}{d x} (\frac{1}{40 ( 2 x - 1 ) ^{5}})

\frac{d}{d x} (\frac{3}{56 ( 2 x - 1 ) ^{7}}) = - \frac{3}{4 ( 2 x - 1 ) ^{8}}

\frac{d}{d x} (\frac{1}{24 ( 2 x - 1 ) ^{6}}) = - \frac{1}{2 ( 2 x - 1 ) ^{7}}

\frac{d}{d x} (\frac{1}{40 ( 2 x - 1 ) ^{5}}) = - \frac{1}{4 ( 2 x - 1 ) ^{6}}

= - \frac{3}{4 ( 2 x - 1 ) ^{8}} - (- \frac{1}{2 ( 2 x - 1 ) ^{7}}) - (- \frac{1}{4 ( 2 x - 1 ) ^{6}})

化简

- \frac{3}{4 ( 2 x - 1 ) ^{8}} - (- \frac{1}{2 ( 2 x - 1 ) ^{7}}) - (- \frac{1}{4 ( 2 x - 1 ) ^{6}}) : \frac{x ^{2} - 1}{( 2 x - 1 ) ^{8}}

= \frac{x ^{2} - 1}{( 2 x - 1 ) ^{8}}

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

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

d er i v a t i v e f (t) = 9 t sin (π t)

\int \frac{cos ( ln ( 9 x ) )}{x} d x

n = 1 \sum \infty \frac{2}{n ( n + 3 )}