de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of x/(tan(3x-1))

Lösung

\frac{d}{d x} (\frac{x}{tan ( 3 x - 1 )})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{tan ( 3 x - 1 )})

Vereinfache

\frac{x}{tan ( 3 x - 1 )} : x cot (3 x - 1)

= \frac{d}{d x} (x cot (3 x - 1))

Wende die Produktregel an:

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

f = x, g = cot (3 x - 1)

= \frac{d x}{d x} cot (3 x - 1) + \frac{d}{d x} (cot (3 x - 1)) x

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

integral of (ln(y))/(xy)

sum from n=1 to infinity of 1/(2n^3)

(\partial)/(\partial x)(x-2|x-2/3 y|)

derivative f(x)=x^4+3x

maclaurin 1/(1-2x)