derivative of log_{3}(3x-7)

Lösung

\frac{d}{d x} (lo g_{3} (3 x - 7))

\frac{3}{ln ( 3 ) ( 3 x - 7 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{3} (3 x - 7))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( 3 x - 7 )}{ln ( 3 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (3 x - 7))

Wende die Kettenregel an:

\frac{1}{3 x - 7} \frac{d}{d x} (3 x - 7)

= \frac{1}{3 x - 7} \frac{d}{d x} (3 x - 7)

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

= \frac{1}{ln ( 3 )} \cdot \frac{1}{3 x - 7} \cdot 3

Vereinfache

\frac{1}{ln ( 3 )} \cdot \frac{1}{3 x - 7} \cdot 3 : \frac{3}{ln ( 3 ) ( 3 x - 7 )}

= \frac{3}{ln ( 3 ) ( 3 x - 7 )}

\frac{d y}{d t} = - \frac{y}{t} + 2

im pl i c i t \frac{d y}{d x}, x y + x = 2

\int_{5}^{8} \frac{5}{x - 5} d x

\frac{\partial}{\partial x} \frac{u}{1 + 2.4 ( \frac{x}{y} )}

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 5 x^{4} y^{7})