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_{8}(sqrt(x+9))

Lösung

\frac{d}{d x} (lo g_{8} (x + 9))

Lösung

\frac{1}{6 ln ( 2 ) ( x + 9 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{8} (x + 9))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( x + 9 )}{ln ( 8 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 8 )} \frac{d}{d x} (ln (x + 9))

Wende die Kettenregel an:

\frac{1}{x + 9} \frac{d}{d x} (x + 9)

= \frac{1}{x + 9} \frac{d}{d x} (x + 9)

\frac{d}{d x} (x + 9) = \frac{1}{2 x + 9}

= \frac{1}{ln ( 8 )} \cdot \frac{1}{x + 9} \cdot \frac{1}{2 x + 9}

Vereinfache

\frac{1}{ln ( 8 )} \cdot \frac{1}{x + 9} \cdot \frac{1}{2 x + 9} : \frac{1}{6 ln ( 2 ) ( x + 9 )}

= \frac{1}{6 ln ( 2 ) ( x + 9 )}

Graph

Beliebte Beispiele

integral of 13sin^2(xco)s^2x

\int 13 sin^{2} (x co) s^{2} x d x

integral of 1/(4e^{-9x)+e^{9x}}

\int \frac{1}{4 e ^{- 9 x} + e ^{9 x}} d x

derivative of 1/(((b/2+x^2+a^2)^{3/2)})

\frac{d}{d x} \frac{1}{( ( \frac{b}{2} + x ) ^{2} + a ^{2} ) ^{\frac{3}{2}}}

integral of e^xsqrt(45+e^x)

\int e^{x} 45 + e^{x} d x

x d y = 8 y d x