derivative (4-sec(x))/(tan(x))

Lösung

ableitung von

\frac{4 - sec ( x )}{tan ( x )}

\frac{- tan ^{2} ( x ) sec ( x ) - sec ^{2} ( x ) ( 4 - sec ( x ) )}{tan ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 - sec ( x )}{tan ( x )})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (4 - sec (x)) = - sec (x) tan (x)

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

= \frac{( - sec ( x ) tan ( x ) ) tan ( x ) - sec ^{2} ( x ) ( 4 - sec ( x ) )}{( tan ( x ) ) ^{2}}

Vereinfache

\frac{( - sec ( x ) tan ( x ) ) tan ( x ) - sec ^{2} ( x ) ( 4 - sec ( x ) )}{tan ^{2} ( x )} : \frac{- tan ^{2} ( x ) sec ( x ) - sec ^{2} ( x ) ( 4 - sec ( x ) )}{tan ^{2} ( x )}

= \frac{- tan ^{2} ( x ) sec ( x ) - sec ^{2} ( x ) ( 4 - sec ( x ) )}{tan ^{2} ( x )}

x \to 0 lim (\frac{1}{ln ( 1 + x )} - \frac{1}{x})

d er i v a t i v e (x^{4} + 3 x)^{- 1}

\frac{d}{d x} (x^{2} + \frac{3456}{x})

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 81 )}

\frac{d}{d x} (\frac{d y}{d x}) + 81 y = 0