derivative of ln(x^3-27x-5)

Lösung

\frac{d}{d x} (ln (x^{3} - 27 x - 5))

\frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{3} - 27 x - 5))

Wende die Kettenregel an:

\frac{1}{x ^{3} - 27 x - 5} \frac{d}{d x} (x^{3} - 27 x - 5)

= \frac{1}{x ^{3} - 27 x - 5} \frac{d}{d x} (x^{3} - 27 x - 5)

\frac{d}{d x} (x^{3} - 27 x - 5) = 3 x^{2} - 27

= \frac{1}{x ^{3} - 27 x - 5} (3 x^{2} - 27)

Vereinfache

\frac{1}{x ^{3} - 27 x - 5} (3 x^{2} - 27) : \frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

= \frac{3 x ^{2} - 27}{x ^{3} - 27 x - 5}

\frac{\frac{d y}{d x}}{2} = y

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

\frac{d}{d x} (\frac{4 x ^{2} + 3 x}{2 x - 7})

d er i v a t i v e 2^{70}

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = 0