derivative of ln(6x^4-9x-3)

Lösung

\frac{d}{d x} (ln (6 x^{4} - 9 x - 3))

\frac{8 x ^{3} - 3}{2 x ^{4} - 3 x - 1}

Schritte zur Lösung

\frac{d}{d x} (ln (6 x^{4} - 9 x - 3))

Wende die Kettenregel an:

\frac{1}{6 x ^{4} - 9 x - 3} \frac{d}{d x} (6 x^{4} - 9 x - 3)

= \frac{1}{6 x ^{4} - 9 x - 3} \frac{d}{d x} (6 x^{4} - 9 x - 3)

\frac{d}{d x} (6 x^{4} - 9 x - 3) = 24 x^{3} - 9

= \frac{1}{6 x ^{4} - 9 x - 3} (24 x^{3} - 9)

Vereinfache

\frac{1}{6 x ^{4} - 9 x - 3} (24 x^{3} - 9) : \frac{8 x ^{3} - 3}{2 x ^{4} - 3 x - 1}

= \frac{8 x ^{3} - 3}{2 x ^{4} - 3 x - 1}

y^{^{''}} + 8 y = 0

\frac{d}{d x} (arctan (9^{x}))

\frac{d x}{d t} + 2 t x^{3} + \frac{x}{t} = 0

\frac{\partial}{\partial x} (3 - (x^{2} + y^{2})^{\frac{1}{3}})

\int 7 e^{- 0.4 x} d x