derivative of x/(tan(x))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{x}{tan ( x )} : x cot (x)

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cot (x)

= \frac{d x}{d x} cot (x) + \frac{d}{d x} (cot (x)) x

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

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

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

Vereinfache

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

in v erse l a pl a ce \frac{2 e ^{- 2 s}}{s ( s + 2 ) ( s + 3 ) ^{2}}

x \to a lim (2 f (x) - 3 g (x))

\frac{d}{d x} ((x^{2} + a^{2})^{e^{x^{2}}})

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

\frac{d}{d x} (lo g_{2} (3 x + 1))