derivative of ln((sin(xcos(x))^2))

Lösung

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

\frac{sin ( 4 x )}{2 sin ^{2} ( x ) cos ^{2} ( x )}

Schritte zur Lösung

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

Vereinfache

ln ((sin (x) cos (x))^{2}) : ln (sin^{2} (x) cos^{2} (x))

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sin^{2} (x) cos^{2} (x)) = \frac{sin ( 4 x )}{2}

= \frac{1}{sin ^{2} ( x ) cos ^{2} ( x )} \cdot \frac{sin ( 4 x )}{2}

Vereinfache

\frac{1}{sin ^{2} ( x ) cos ^{2} ( x )} \cdot \frac{sin ( 4 x )}{2} : \frac{sin ( 4 x )}{2 sin ^{2} ( x ) cos ^{2} ( x )}

= \frac{sin ( 4 x )}{2 sin ^{2} ( x ) cos ^{2} ( x )}

\int x^{2} in (x) d x

t an g e n t f (x) = sin (sin (x)), (π, 0)

\int \frac{9 x ( 6 x ^{2} + 5 ) ^{\frac{1}{2}}}{2} d x

\int \frac{1}{19 y} d y

in v erse l a pl a ce \frac{4}{s ^{2} + 7 s + 12}