derivative of (e^{-2x}/(\sqrt[3]{6x-1)})

Lösung

\frac{d}{d x} (\frac{e ^{- 2 x}}{3 6 x - 1})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{- 2 x}}{3 6 x - 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{- 2 x} ) 3 6 x - 1 - \frac{d}{d x} ( 3 6 x - 1 ) e ^{- 2 x}}{( 3 6 x - 1 ) ^{2}}

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

\frac{d}{d x} (3 6 x - 1) = \frac{2}{( 6 x - 1 ) ^{\frac{2}{3}}}

= \frac{( - 2 e ^{- 2 x} ) 3 6 x - 1 - \frac{2}{( 6 x - 1 ) ^{\frac{2}{3}}} e ^{- 2 x}}{( 3 6 x - 1 ) ^{2}}

Vereinfache

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

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

y^{^{''}} + y^{^{'}} + 6 y = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{8 + e ^{x}}

d er i v a t i v e (4^{x})^{9}

im pl i c i t \frac{d y}{d x}, 4^{x} = 2 x y

\int \frac{x}{x + 4} d x