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

Lösung

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

\frac{\partial}{\partial x} (12 x y)

\frac{d}{d x} (\frac{x + 4}{x - 4})

\int - cos^{2} (x) sin (x) d x

\int (5 cos (x) + 4 sin (x)) d x

\frac{d}{d x} (\frac{x}{tan ( 3 x - 1 )})