derivative of (x^5/(1-x^4))

Lösung

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

\frac{5 x ^{4} - x ^{8}}{( 1 - x ^{4} ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{5 x ^{4} ( 1 - x ^{4} ) - ( - 4 x ^{3} ) x ^{5}}{( 1 - x ^{4} ) ^{2}} : \frac{5 x ^{4} - x ^{8}}{( 1 - x ^{4} ) ^{2}}

= \frac{5 x ^{4} - x ^{8}}{( 1 - x ^{4} ) ^{2}}

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

\int \frac{1}{( 3 - 4 x )} d x

\int 10 x^{4} + 20 x + 8 d x

h \to 0 lim (\frac{( 1 + h ) ^{4} - 1}{h})

\frac{d}{d x} (lo g_{e} (2 x))