derivative of (csc(x)/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d x}{d x} = 1

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

Vereinfache

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

l a pl a ce t r an s f or m t cos (4 t)

y^{^{'}} = (0.5 + sin (t)) (\frac{y}{5})

t a y l or e^{- x}, x = 0

\int sec^{4} (\frac{x}{3}) d x

d er i v a t i v e y = x^{2} e^{x} - 2 x e^{x} + 5 e^{x}