derivative of (x^6/(4-x^5))

Lösung

\frac{d}{d x} (\frac{x ^{6}}{4 - x ^{5}})

\frac{24 x ^{5} - x ^{10}}{( 4 - x ^{5} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{6}}{4 - x ^{5}})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

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

Vereinfache

\frac{6 x ^{5} ( 4 - x ^{5} ) - ( - 5 x ^{4} ) x ^{6}}{( 4 - x ^{5} ) ^{2}} : \frac{24 x ^{5} - x ^{10}}{( 4 - x ^{5} ) ^{2}}

= \frac{24 x ^{5} - x ^{10}}{( 4 - x ^{5} ) ^{2}}

\frac{d}{d x} (3 x^{8})

\int e^{2 x} 1 + e^{2 x} d x

\frac{\partial}{\partial x} (\frac{6 y}{( x + y ) ^{2}})

x \to - \infty lim (2 - x)

\int_{1}^{5} \frac{x}{2 x + 1} d x