derivative of log_{3}(x+3)

Lösung

\frac{d}{d x} (lo g_{3} (x + 3))

\frac{1}{ln ( 3 ) ( x + 3 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{3} (x + 3))

Wende die log Regel an:

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

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

\frac{1}{x + 3} \frac{d}{d x} (x + 3)

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

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

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

Vereinfache

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

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

\int 6 x^{5} (x^{6})^{5} d x

\int \frac{3 t ^{2} + 2}{( t ^{3} + 2 t + 3 ) ^{5}} d t

\frac{\partial}{\partial y} (cos (x + y))

\frac{d}{d x} (36 - x^{2})

\frac{\partial}{\partial x} (y^{4} cos (4 x))