derivative of arctan(sin(2x))

Lösung

\frac{d}{d x} (arctan (sin (2 x)))

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

Schritte zur Lösung

\frac{d}{d x} (arctan (sin (2 x)))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int 1 - 4 (\frac{1}{2} sin (x))^{2} d x

d er i v a t i v e ln (1 - 5 x)

l a pl a ce t r an s f or m f (t) = e^{2 (t - 2)}

d er i v a t i v e f (x) = \frac{1 + x}{( 2 x ^{2} + 1 ) ^{2}}

\frac{d}{d t} (t^{3} - 5 t^{2} + 9 t)