derivative of ln^3(3x^2-5)

Lösung

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

\frac{18 x ln ^{2} ( 3 x ^{2} - 5 )}{3 x ^{2} - 5}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (ln (3 x^{2} - 5)) = \frac{6 x}{3 x ^{2} - 5}

= 3 (ln (3 x^{2} - 5))^{2} \frac{6 x}{3 x ^{2} - 5}

Vereinfache

3 ln^{2} (3 x^{2} - 5) \frac{6 x}{3 x ^{2} - 5} : \frac{18 x ln ^{2} ( 3 x ^{2} - 5 )}{3 x ^{2} - 5}

= \frac{18 x ln ^{2} ( 3 x ^{2} - 5 )}{3 x ^{2} - 5}

\int (x^{2} + 2)^{3} d x

x \to 0 lim ((x - 4)^{3})

y^{^{'}} = \frac{( y ^{2} + 1 )}{x}

x \to 1 lim (\frac{1 - \frac{2 l n ( 1 + x )}{x}}{x})

\int \frac{12}{x} + 12 x d x