derivative arctan(sin(2x))

Lösung

ableitung von

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}

t an g e n t f (x) = x, at x = \frac{1}{81}

d er i v a t i v e 5 \frac{1}{x}

\int_{0}^{3.5} 90 x d x

n = 1 \sum \infty \frac{1}{2 n ^{2}}

ma c l a u r in x^{2} e^{x} - x^{3} - x^{2}