derivative of sqrt(cos(e^{x^2cos(x))})

Lösung

\frac{d}{d x} (cos (e^{x^{2} c o s (x)}))

- \frac{e ^{x^{2} c o s (x)} sin ( e ^{x^{2} c o s (x)} ) ( 2 x cos ( x ) - x ^{2} sin ( x ) )}{2 cos ( e ^{x^{2} c o s (x)} )}

Schritte zur Lösung

\frac{d}{d x} (cos (e^{x^{2} c o s (x)}))

Wende die Kettenregel an:

\frac{1}{2 cos ( e ^{x^{2} c o s (x)} )} \frac{d}{d x} (cos (e^{x^{2} c o s (x)}))

= \frac{1}{2 cos ( e ^{x^{2} c o s (x)} )} \frac{d}{d x} (cos (e^{x^{2} c o s (x)}))

\frac{d}{d x} (cos (e^{x^{2} c o s (x)})) = - sin (e^{x^{2} c o s (x)}) e^{x^{2} c o s (x)} (2 x cos (x) - x^{2} sin (x))

= \frac{1}{2 cos ( e ^{x^{2} c o s (x)} )} (- sin (e^{x^{2} c o s (x)}) e^{x^{2} c o s (x)} (2 x cos (x) - x^{2} sin (x)))

Vereinfache

\frac{1}{2 cos ( e ^{x^{2} c o s (x)} )} (- sin (e^{x^{2} c o s (x)}) e^{x^{2} c o s (x)} (2 x cos (x) - x^{2} sin (x))) : - \frac{e ^{x^{2} c o s (x)} sin ( e ^{x^{2} c o s (x)} ) ( 2 x cos ( x ) - x ^{2} sin ( x ) )}{2 cos ( e ^{x^{2} c o s (x)} )}

= - \frac{e ^{x^{2} c o s (x)} sin ( e ^{x^{2} c o s (x)} ) ( 2 x cos ( x ) - x ^{2} sin ( x ) )}{2 cos ( e ^{x^{2} c o s (x)} )}

n = 1 \sum \infty \frac{4 ^{n}}{5 ^{n}}

d er i v a t i v e 8 t^{2} - t

d er i v a t i v e (3 x + 5)^{2}

(2 x - 1) d x + (7 y + 8) d y = 0

x \to - 5 lim (4)