derivative of ((2x-3^{-3})/((2-3x)^2))

Lösung

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

- \frac{30 ( x - 1 )}{( 2 x - 3 ) ^{4} ( 3 x - 2 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} ((2 x - 3)^{- 3}) = - \frac{6}{( 2 x - 3 ) ^{4}}

\frac{d}{d x} ((2 - 3 x)^{2}) = - 6 (2 - 3 x)

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

Vereinfache

\frac{( - \frac{6}{( 2 x - 3 ) ^{4}} ) ( 2 - 3 x ) ^{2} - ( - 6 ( 2 - 3 x ) ) ( 2 x - 3 ) ^{- 3}}{( ( 2 - 3 x ) ^{2} ) ^{2}} : - \frac{30 ( x - 1 )}{( 2 x - 3 ) ^{4} ( 3 x - 2 ) ^{3}}

= - \frac{30 ( x - 1 )}{( 2 x - 3 ) ^{4} ( 3 x - 2 ) ^{3}}

x \to 0 lim (\frac{x ^{4} + 1}{x ^{2}})

\int sin^{5} (8 x) d x

\frac{d}{d x} (- 9 sin (x))

h \to \frac{1}{2} lim (\frac{8 h ^{3} - 1}{1 - 2 h})

d er i v a t i v e \frac{8}{tan ^{3} ( \frac{x}{2} )}