derivative of ({f}(x)/(x^9))

Lösung

\frac{d}{d x} (\frac{f ( x )}{x ^{9}})

\frac{x \frac{d}{d x} ( f ( x ) ) - 9 f ( x )}{x ^{10}}

Schritte zur Lösung

\frac{d}{d x} (\frac{f ( x )}{x ^{9}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( f ( x ) ) x ^{9} - \frac{d}{d x} ( x ^{9} ) f ( x )}{( x ^{9} ) ^{2}}

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{\frac{d}{d x} ( f ( x ) ) x ^{9} - 9 x ^{8} f ( x )}{( x ^{9} ) ^{2}}

Vereinfache

\frac{\frac{d}{d x} ( f ( x ) ) x ^{9} - 9 x ^{8} f ( x )}{( x ^{9} ) ^{2}} : \frac{x \frac{d}{d x} ( f ( x ) ) - 9 f ( x )}{x ^{10}}

= \frac{x \frac{d}{d x} ( f ( x ) ) - 9 f ( x )}{x ^{10}}

d er i v a t i v e 5 sec (8 x)

x \to 0 lim (\frac{x ^{2} - 2 x}{x})

d er i v a t i v e arctan (\frac{1}{x})

t a y l or \frac{1}{x + 4}, 0

(x, y, z) \to (π, 0, \frac{1}{3}) lim (e^{y^{2}} tan (x z))