derivative y=(f(x))/(x^5)

Lösung

ableitung von

y = \frac{f ( x )}{x ^{5}}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{f ( x )}{x ^{5}})

Wende die Quotientenregel an:

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

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

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

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

Vereinfache

\frac{\frac{df}{d x} x ^{5} - 5 x ^{4} f ( x )}{( x ^{5} ) ^{2}} : \frac{x \frac{df}{d x} - 5 f ( x )}{x ^{6}}

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

d er i v a t i v e 2 tan^{2} (7 x)

(2 x y + 3) d x + (x^{2} - 1) d y = 0

3 x y^{^{'}} + 7 y = 0

d er i v a t i v e \frac{e ^{10 x} + e ^{- 10 x}}{x}

\frac{d}{d x} (2 (ln (x)))