derivative ln(x^3sin^2(x))

Lösung

ableitung von

ln (x^{3} sin^{2} (x))

\frac{3 sin ^{2} ( x ) + x sin ( 2 x )}{x sin ^{2} ( x )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{x ^{3} sin ^{2} ( x )} (3 x^{2} sin^{2} (x) + sin (2 x) x^{3})

Vereinfache

\frac{1}{x ^{3} sin ^{2} ( x )} (3 x^{2} sin^{2} (x) + sin (2 x) x^{3}) : \frac{3 sin ^{2} ( x ) + x sin ( 2 x )}{x sin ^{2} ( x )}

= \frac{3 sin ^{2} ( x ) + x sin ( 2 x )}{x sin ^{2} ( x )}

\int_{- \infty}^{2} \frac{2}{x ^{2} + 4} d x

t an g e n t f (x) = 2 x - x^{2}

\int cos (x) sin^{5} (x) d x

a re a 3 - x, - 4 \leq x \leq 2

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