derivative of log_{3}(\sqrt[5]{x+2})

Lösung

\frac{d}{d x} (lo g_{3} (5 x + 2))

\frac{1}{5 ln ( 3 ) 5 x + 2 ( x + 2 ) ^{\frac{4}{5}}}

Schritte zur Lösung

\frac{d}{d x} (lo g_{3} (5 x + 2))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( 5 x + 2 )}{ln ( 3 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (5 x + 2))

Wende die Kettenregel an:

\frac{1}{5 x + 2} \frac{d}{d x} (5 x + 2)

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

\frac{d}{d x} (5 x + 2) = \frac{1}{5 ( x + 2 ) ^{\frac{4}{5}}}

= \frac{1}{ln ( 3 )} \cdot \frac{1}{5 x + 2} \cdot \frac{1}{5 ( x + 2 ) ^{\frac{4}{5}}}

Vereinfache

\frac{1}{ln ( 3 )} \cdot \frac{1}{5 x + 2} \cdot \frac{1}{5 ( x + 2 ) ^{\frac{4}{5}}} : \frac{1}{5 ln ( 3 ) 5 x + 2 ( x + 2 ) ^{\frac{4}{5}}}

= \frac{1}{5 ln ( 3 ) 5 x + 2 ( x + 2 ) ^{\frac{4}{5}}}

y^{2} \cdot (\frac{d y}{d x}) + y^{3} = 1

\int \frac{x ^{3} + 1}{x ^{2} + 5 x + 6} d x

\frac{d}{d x} (\frac{1}{2 x ^{2} + 4})

\frac{d}{d x} (750 + 12 x - 0.08 x^{7})

d er i v a t i v e x^{4} + 8 x + 6