derivative of (csc(x)/(1+csc(x)))

Lösung

\frac{d}{d x} (\frac{csc ( x )}{1 + csc ( x )})

- \frac{cot ( x ) csc ( x )}{( 1 + csc ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{csc ( x )}{1 + csc ( x )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( csc ( x ) ) ( 1 + csc ( x ) ) - \frac{d}{d x} ( 1 + csc ( x ) ) csc ( x )}{( 1 + csc ( x ) ) ^{2}}

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

\frac{d}{d x} (1 + csc (x)) = - cot (x) csc (x)

= \frac{( - cot ( x ) csc ( x ) ) ( 1 + csc ( x ) ) - ( - cot ( x ) csc ( x ) ) csc ( x )}{( 1 + csc ( x ) ) ^{2}}

Vereinfache

\frac{( - cot ( x ) csc ( x ) ) ( 1 + csc ( x ) ) - ( - cot ( x ) csc ( x ) ) csc ( x )}{( 1 + csc ( x ) ) ^{2}} : - \frac{cot ( x ) csc ( x )}{( 1 + csc ( x ) ) ^{2}}

= - \frac{cot ( x ) csc ( x )}{( 1 + csc ( x ) ) ^{2}}

y^{^{''}} + 4 y = e^{4 x}

\int e^{e^{x}} d x

\frac{d}{d x} (\frac{2 x - 1}{x - 1})

\frac{\partial}{\partial x} (- x e^{- x y})

l a pl a ce t r an s f or m - 1