de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of log_{5}(2x^2)

Lösung

\frac{d}{d x} (lo g_{5} (2 x^{2}))

Lösung

\frac{2}{ln ( 5 ) x}

Schritte zur Lösung

\frac{d}{d x} (lo g_{5} (2 x^{2}))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 2 x ^{2} )}{ln ( 5 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (2 x^{2}))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x^{2}) = 4 x

= \frac{1}{ln ( 5 )} \cdot \frac{1}{2 x ^{2}} \cdot 4 x

Vereinfache

\frac{1}{ln ( 5 )} \cdot \frac{1}{2 x ^{2}} \cdot 4 x : \frac{2}{ln ( 5 ) x}

= \frac{2}{ln ( 5 ) x}

Graph

Beliebte Beispiele

d/(dy)(e^ycos(y))

\frac{d}{d y} (e^{y} cos (y))

integral of tan^2(x)sec^6(x)

\int tan^{2} (x) sec^{6} (x) d x

integral of x(x^2+1)^{100}

\int x (x^{2} + 1)^{100} d x

longdivision (x^2-10x+65)/(x-8)

l o n g d i v i s i o n \frac{x ^{2} - 10 x + 65}{x - 8}

sum from n=0 to infinity of 1/((2n-1)^2)

n = 0 \sum \infty \frac{1}{( 2 n - 1 ) ^{2}}