derivative of sqrt(sin(e^{x^3sin(x))})

Lösung

\frac{d}{d x} (sin (e^{x^{3} s i n (x)}))

\frac{e ^{x^{3} s i n (x)} cos ( e ^{x^{3} s i n (x)} ) ( 3 x ^{2} sin ( x ) + x ^{3} cos ( x ) )}{2 sin ( e ^{x^{3} s i n (x)} )}

Schritte zur Lösung

\frac{d}{d x} (sin (e^{x^{3} s i n (x)}))

Wende die Kettenregel an:

\frac{1}{2 sin ( e ^{x^{3} s i n (x)} )} \frac{d}{d x} (sin (e^{x^{3} s i n (x)}))

= \frac{1}{2 sin ( e ^{x^{3} s i n (x)} )} \frac{d}{d x} (sin (e^{x^{3} s i n (x)}))

\frac{d}{d x} (sin (e^{x^{3} s i n (x)})) = cos (e^{x^{3} s i n (x)}) e^{x^{3} s i n (x)} (3 x^{2} sin (x) + cos (x) x^{3})

= \frac{1}{2 sin ( e ^{x^{3} s i n (x)} )} cos (e^{x^{3} s i n (x)}) e^{x^{3} s i n (x)} (3 x^{2} sin (x) + cos (x) x^{3})

Vereinfache

\frac{1}{2 sin ( e ^{x^{3} s i n (x)} )} cos (e^{x^{3} s i n (x)}) e^{x^{3} s i n (x)} (3 x^{2} sin (x) + cos (x) x^{3}) : \frac{e ^{x^{3} s i n (x)} cos ( e ^{x^{3} s i n (x)} ) ( 3 x ^{2} sin ( x ) + x ^{3} cos ( x ) )}{2 sin ( e ^{x^{3} s i n (x)} )}

= \frac{e ^{x^{3} s i n (x)} cos ( e ^{x^{3} s i n (x)} ) ( 3 x ^{2} sin ( x ) + x ^{3} cos ( x ) )}{2 sin ( e ^{x^{3} s i n (x)} )}

\frac{d}{d x} (x^{2} - 8 x + 12)

\int \frac{1}{8 - 3 x} d x

\int_{0}^{1} - ln (x) d x

\frac{d y}{d x} = - y (x + 1)

d er i v a t i v e x + 4 x + 2