de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of 2sqrt(x)ln(x)

Lösung

\frac{d}{d x} (2 x ln (x))

Lösung

2 (\frac{ln ( x )}{2 x} + \frac{1}{x})

Schritte zur Lösung

\frac{d}{d x} (2 x ln (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x, g = ln (x)

= 2 (\frac{d}{d x} (x) ln (x) + \frac{d}{d x} (ln (x)) x)

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

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

= 2 (\frac{1}{2 x} ln (x) + \frac{1}{x} x)

Vereinfache

2 (\frac{1}{2 x} ln (x) + \frac{1}{x} x) : 2 (\frac{ln ( x )}{2 x} + \frac{1}{x})

= 2 (\frac{ln ( x )}{2 x} + \frac{1}{x})

Graph

Beliebte Beispiele

tangent (x-y-1)^3=x,(1,-1)

t an g e n t (x - y - 1)^{3} = x, (1, - 1)

y^{''}+y^'=3sin(4x)

y^{^{''}} + y^{^{'}} = 3 sin (4 x)

limit as n approaches infinity of (n!)^n

n \to \infty lim ((n!)^{n})

integral of ((2x+7)/(x^2+2x+5))

\int (\frac{2 x + 7}{x ^{2} + 2 x + 5}) d x

tangent (3x)/((x+1)^2)(0)

t an g e n t \frac{3 x}{( x + 1 ) ^{2}} (0)