derivative (x^6)/(2-x^5)

Lösung

ableitung von

\frac{x ^{6}}{2 - x ^{5}}

\frac{12 x ^{5} - x ^{10}}{( 2 - x ^{5} ) ^{2}}

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{6 x ^{5} ( 2 - x ^{5} ) - ( - 5 x ^{4} ) x ^{6}}{( 2 - x ^{5} ) ^{2}} : \frac{12 x ^{5} - x ^{10}}{( 2 - x ^{5} ) ^{2}}

= \frac{12 x ^{5} - x ^{10}}{( 2 - x ^{5} ) ^{2}}

d er i v a t i v e f (x) = \frac{5}{4} x^{\frac{4}{3}}

x \to 6 - lim (\frac{- 6}{x + 6})

p a r t ia l f r a c t i o n \frac{x ^{3}}{x - 2}

\frac{d y}{d x} = y^{2} + a^{2}

\int \frac{e ^{x}}{e ^{2 x} + 9} d x