derivative of (csc(3x)/(x^3+1))

Lösung

\frac{d}{d x} (\frac{csc ( 3 x )}{x ^{3} + 1})

\frac{- 3 cot ( 3 x ) csc ( 3 x ) ( x ^{3} + 1 ) - 3 x ^{2} csc ( 3 x )}{( x ^{3} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{csc ( 3 x )}{x ^{3} + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( csc ( 3 x ) ) ( x ^{3} + 1 ) - \frac{d}{d x} ( x ^{3} + 1 ) csc ( 3 x )}{( x ^{3} + 1 ) ^{2}}

\frac{d}{d x} (csc (3 x)) = - cot (3 x) csc (3 x) \cdot 3

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

= \frac{( - cot ( 3 x ) csc ( 3 x ) \cdot 3 ) ( x ^{3} + 1 ) - 3 x ^{2} csc ( 3 x )}{( x ^{3} + 1 ) ^{2}}

Vereinfache

= \frac{- 3 cot ( 3 x ) csc ( 3 x ) ( x ^{3} + 1 ) - 3 x ^{2} csc ( 3 x )}{( x ^{3} + 1 ) ^{2}}

\int t e^{2 t} d t

\int sin^{4} (3 t) d t

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

\frac{\partial}{\partial x} (x^{2} (y - x))

d er i v a t i v e 9 x y