derivative of sqrt(cos(e^{x^5sin(x))})

Lösung

\frac{d}{d x} (cos (e^{x^{5} s i n (x)}))

- \frac{e ^{x^{5} s i n (x)} sin ( e ^{x^{5} s i n (x)} ) ( 5 x ^{4} sin ( x ) + x ^{5} cos ( x ) )}{2 cos ( e ^{x^{5} s i n (x)} )}

Schritte zur Lösung

\frac{d}{d x} (cos (e^{x^{5} s i n (x)}))

Wende die Kettenregel an:

\frac{1}{2 cos ( e ^{x^{5} s i n (x)} )} \frac{d}{d x} (cos (e^{x^{5} s i n (x)}))

= \frac{1}{2 cos ( e ^{x^{5} s i n (x)} )} \frac{d}{d x} (cos (e^{x^{5} s i n (x)}))

\frac{d}{d x} (cos (e^{x^{5} s i n (x)})) = - sin (e^{x^{5} s i n (x)}) e^{x^{5} s i n (x)} (5 x^{4} sin (x) + cos (x) x^{5})

= \frac{1}{2 cos ( e ^{x^{5} s i n (x)} )} (- sin (e^{x^{5} s i n (x)}) e^{x^{5} s i n (x)} (5 x^{4} sin (x) + cos (x) x^{5}))

Vereinfache

\frac{1}{2 cos ( e ^{x^{5} s i n (x)} )} (- sin (e^{x^{5} s i n (x)}) e^{x^{5} s i n (x)} (5 x^{4} sin (x) + cos (x) x^{5})) : - \frac{e ^{x^{5} s i n (x)} sin ( e ^{x^{5} s i n (x)} ) ( 5 x ^{4} sin ( x ) + x ^{5} cos ( x ) )}{2 cos ( e ^{x^{5} s i n (x)} )}

= - \frac{e ^{x^{5} s i n (x)} sin ( e ^{x^{5} s i n (x)} ) ( 5 x ^{4} sin ( x ) + x ^{5} cos ( x ) )}{2 cos ( e ^{x^{5} s i n (x)} )}

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