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

Lösung

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

\frac{5 x ^{2} - 9}{x ( x ^{2} - 3 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{5} - 3 x^{3}) = 5 x^{4} - 9 x^{2}

= \frac{1}{x ^{5} - 3 x ^{3}} (5 x^{4} - 9 x^{2})

Vereinfache

\frac{1}{x ^{5} - 3 x ^{3}} (5 x^{4} - 9 x^{2}) : \frac{5 x ^{2} - 9}{x ( x ^{2} - 3 )}

= \frac{5 x ^{2} - 9}{x ( x ^{2} - 3 )}

n = 0 \sum \infty \frac{1}{6 ^{n}}

x y^{^{'}} + 2 y = 12 x^{2}

\frac{d}{d t} (sin (t^{3}))

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

d er i v a t i v e f (x) = \frac{4}{( x ^{2} + 6 x ) ^{3}}