derivative f(x)=arctan(sin(4x))

Lösung

ableitung von

f (x) = arctan (sin (4 x))

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

Schritte zur Lösung

\frac{d}{d x} (arctan (sin (4 x)))

Wende die Kettenregel an:

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

= \frac{1}{( sin ( 4 x ) ) ^{2} + 1} \frac{d}{d x} (sin (4 x))

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

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

Vereinfache

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

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

\int x y e^{x y^{2}} d y

\frac{d}{d x} (\frac{6 x}{x ^{2} - 4})

\int \frac{1}{2 x + x ^{3}} d x

\int \frac{6}{x ^{2} + 16} d x

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