derivative of arctan(sin(ln(x^3)))

Lösung

\frac{d}{d x} (arctan (sin (ln (x^{3}))))

\frac{3 cos ( 3 ln ( x ) )}{x ( sin ^{2} ( 3 ln ( x ) ) + 1 )}

Schritte zur Lösung

\frac{d}{d x} (arctan (sin (ln (x^{3}))))

Wende die Kettenregel an:

\frac{1}{( sin ( ln ( x ^{3} ) ) ) ^{2} + 1} \frac{d}{d x} (sin (ln (x^{3})))

= \frac{1}{( sin ( ln ( x ^{3} ) ) ) ^{2} + 1} \frac{d}{d x} (sin (ln (x^{3})))

\frac{d}{d x} (sin (ln (x^{3}))) = \frac{3 cos ( ln ( x ^{3} ) )}{x}

= \frac{1}{( sin ( ln ( x ^{3} ) ) ) ^{2} + 1} \cdot \frac{3 cos ( ln ( x ^{3} ) )}{x}

Vereinfache

\frac{1}{sin ^{2} ( ln ( x ^{3} ) ) + 1} \cdot \frac{3 cos ( ln ( x ^{3} ) )}{x} : \frac{3 cos ( 3 ln ( x ) )}{x ( sin ^{2} ( 3 ln ( x ) ) + 1 )}

= \frac{3 cos ( 3 ln ( x ) )}{x ( sin ^{2} ( 3 ln ( x ) ) + 1 )}

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

s l o p e y = 2 x^{3} - x^{2} + 3

\frac{d y}{d x} = 4 x y

\int \frac{1}{1 + 5 x ^{2}} d x

d er i v a t i v e 3 - 5 x