derivative log_{8}(5x^3+3x)

Lösung

ableitung von

lo g_{8} (5 x^{3} + 3 x)

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

Schritte zur Lösung

\frac{d}{d x} (lo g_{8} (5 x^{3} + 3 x))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( 5 x ^{3} + 3 x )}{ln ( 8 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 8 )} \frac{d}{d x} (ln (5 x^{3} + 3 x))

Wende die Kettenregel an:

\frac{1}{5 x ^{3} + 3 x} \frac{d}{d x} (5 x^{3} + 3 x)

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

\frac{d}{d x} (5 x^{3} + 3 x) = 15 x^{2} + 3

= \frac{1}{ln ( 8 )} \cdot \frac{1}{5 x ^{3} + 3 x} (15 x^{2} + 3)

Vereinfache

\frac{1}{ln ( 8 )} \cdot \frac{1}{5 x ^{3} + 3 x} (15 x^{2} + 3) : \frac{5 x ^{2} + 1}{ln ( 2 ) x ( 5 x ^{2} + 3 )}

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

\int_{0}^{2} (1 + x^{2}) d x

\frac{\partial}{\partial x} (\frac{x ^{2}}{16 - y ^{2}})

\int \frac{1}{tan ( 5 x )} d x

t an g e n t f (x) = \frac{1}{2 + 3 x}, (1, \frac{1}{5})

l a pl a ce t r an s f or m e^{- 2 t} t