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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{x x ^{2} - 3} \frac{d}{d x} (x x^{2} - 3)

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

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

= \frac{1}{x x ^{2} - 3} \cdot \frac{2 x ^{2} - 3}{x ^{2} - 3}

Vereinfache

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

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

\frac{d}{d x} (\frac{2 x + 3}{x + 1})

d er i v a t i v e (3 x^{6} + 8 x^{3})^{4}

\int_{- 1}^{- 0.2588} e^{- i π^{2} w s} d w

k = 2 \sum \infty k^{k}

a re a 7 x e^{- x^{2}}, y = 0, 0 \leq x \leq 1