derivative y=(f(x))/(x^6)

Lösung

ableitung von

y = \frac{f ( x )}{x ^{6}}

\frac{x \frac{df}{d x} - 6 f ( x )}{x ^{7}}

Schritte zur Lösung

\frac{d}{d x} (\frac{f ( x )}{x ^{6}})

Wende die Quotientenregel an:

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

= \frac{\frac{df}{d x} x ^{6} - \frac{d}{d x} ( x ^{6} ) f ( x )}{( x ^{6} ) ^{2}}

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

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

Vereinfache

\frac{\frac{df}{d x} x ^{6} - 6 x ^{5} f ( x )}{( x ^{6} ) ^{2}} : \frac{x \frac{df}{d x} - 6 f ( x )}{x ^{7}}

= \frac{x \frac{df}{d x} - 6 f ( x )}{x ^{7}}

\int_{0}^{1} x - x^{k} d x

d er i v a t i v e 3

\frac{d}{d x} (arctan (\frac{x}{2000}))

\int x \cdot \frac{e ^{x}}{2 x} d x

\frac{d}{d x} (x e^{3 z (x)})