derivative of arctan(sin(7x))

Lösung

\frac{d}{d x} (arctan (sin (7 x)))

\frac{7 cos ( 7 x )}{sin ^{2} ( 7 x ) + 1}

Schritte zur Lösung

\frac{d}{d x} (arctan (sin (7 x)))

Wende die Kettenregel an:

\frac{1}{( sin ( 7 x ) ) ^{2} + 1} \frac{d}{d x} (sin (7 x))

= \frac{1}{( sin ( 7 x ) ) ^{2} + 1} \frac{d}{d x} (sin (7 x))

\frac{d}{d x} (sin (7 x)) = cos (7 x) \cdot 7

= \frac{1}{( sin ( 7 x ) ) ^{2} + 1} cos (7 x) \cdot 7

Vereinfache

\frac{1}{sin ^{2} ( 7 x ) + 1} cos (7 x) \cdot 7 : \frac{7 cos ( 7 x )}{sin ^{2} ( 7 x ) + 1}

= \frac{7 cos ( 7 x )}{sin ^{2} ( 7 x ) + 1}

\int o d o

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 8

\frac{d}{d x} (x arcsec (x^{3}))

in v erse l a pl a ce \frac{( 6 + 6 s )}{2 s ^{2} + 1}

d er i v a t i v e 9 x^{\frac{1}{2}}