derivative (tan(3x))/(x^2)

Lösung

ableitung von

\frac{tan ( 3 x )}{x ^{2}}

\frac{3 x sec ^{2} ( 3 x ) - 2 tan ( 3 x )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{tan ( 3 x )}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( tan ( 3 x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) tan ( 3 x )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (tan (3 x)) = sec^{2} (3 x) \cdot 3

\frac{d}{d x} (x^{2}) = 2 x

= \frac{sec ^{2} ( 3 x ) \cdot 3 x ^{2} - 2 x tan ( 3 x )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{sec ^{2} ( 3 x ) \cdot 3 x ^{2} - 2 x tan ( 3 x )}{( x ^{2} ) ^{2}} : \frac{3 x sec ^{2} ( 3 x ) - 2 tan ( 3 x )}{x ^{3}}

= \frac{3 x sec ^{2} ( 3 x ) - 2 tan ( 3 x )}{x ^{3}}

\int \frac{24 x ^{6} - 24 x ^{4} + x}{x} d x

x d y = d x

\frac{d}{d x} (ln (\frac{1 + x}{1 - x}))

\frac{d}{d x} (sin (3 x y))

d er i v a t i v e y = 4 sec (5 x)