de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of (ln(3x)/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{ln ( 3 x )}{x})

Lösung

\frac{2 - ln ( 3 x )}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( 3 x )}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ln ( 3 x ) ) x - \frac{d}{d x} ( x ) ln ( 3 x )}{( x ) ^{2}}

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{\frac{1}{x} x - \frac{1}{2 x} ln ( 3 x )}{( x ) ^{2}}

Vereinfache

\frac{\frac{1}{x} x - \frac{1}{2 x} ln ( 3 x )}{( x ) ^{2}} : \frac{2 - ln ( 3 x )}{2 x x}

= \frac{2 - ln ( 3 x )}{2 x x}

Graph

Beliebte Beispiele

3y^{''}+13y^'+4=0,y(0)=0,y^'(0)=0

3 y^{^{''}} + 13 y^{^{'}} + 4 = 0, y (0) = 0, y^{^{'}} (0) = 0

derivative of 3(7-3x^3^3)

\frac{d}{d x} (3 (7 - 3 x^{3})^{3})

-(1+y^2)^{1/2}dx+4xydy=0

- (1 + y^{2})^{\frac{1}{2}} d x + 4 x y d y = 0

derivative of 1+csc(x)

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

limit as x approaches-infinity of-xe^x

x \to - \infty lim (- x e^{x})