derivative of (2e^x-x^5/(1-3x^5))

Lösung

\frac{d}{d x} (\frac{2 e ^{x} - x ^{5}}{1 - 3 x ^{5}})

\frac{- 6 e ^{x} x ^{5} - 5 x ^{4} + 30 e ^{x} x ^{4} + 2 e ^{x}}{( 1 - 3 x ^{5} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 e ^{x} - x ^{5}}{1 - 3 x ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 e ^{x} - x ^{5} ) ( 1 - 3 x ^{5} ) - \frac{d}{d x} ( 1 - 3 x ^{5} ) ( 2 e ^{x} - x ^{5} )}{( 1 - 3 x ^{5} ) ^{2}}

\frac{d}{d x} (2 e^{x} - x^{5}) = 2 e^{x} - 5 x^{4}

\frac{d}{d x} (1 - 3 x^{5}) = - 15 x^{4}

= \frac{( 2 e ^{x} - 5 x ^{4} ) ( 1 - 3 x ^{5} ) - ( - 15 x ^{4} ) ( 2 e ^{x} - x ^{5} )}{( 1 - 3 x ^{5} ) ^{2}}

Vereinfache

\frac{( 2 e ^{x} - 5 x ^{4} ) ( 1 - 3 x ^{5} ) - ( - 15 x ^{4} ) ( 2 e ^{x} - x ^{5} )}{( 1 - 3 x ^{5} ) ^{2}} : \frac{- 6 e ^{x} x ^{5} - 5 x ^{4} + 30 e ^{x} x ^{4} + 2 e ^{x}}{( 1 - 3 x ^{5} ) ^{2}}

= \frac{- 6 e ^{x} x ^{5} - 5 x ^{4} + 30 e ^{x} x ^{4} + 2 e ^{x}}{( 1 - 3 x ^{5} ) ^{2}}

\int \frac{2 x - 3}{6} d x

\frac{d}{d x} (\frac{x ^{2}}{x ^{4}})

\frac{d}{d x} (\frac{1}{1 - x})

\int coth^{2} (x) d x

\int \frac{1}{9 - x ^{2}} d x