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

Lösung

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

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

Schritte zur Lösung

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

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

Vereinfache

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

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

\int cos^{2} (4 x) sin^{3} (4 x) d x

x \to \infty lim (7^{2 x})

t an g e n t x^{4} + 4 x^{2} - x

\frac{d ^{2}}{d x ^{2}} (sin (7 x))

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