derivative of sqrt(cos(e^{x^4cos(x))})

Lösung

\frac{d}{d x} (cos (e^{x^{4} c o s (x)}))

- \frac{e ^{x^{4} c o s (x)} sin ( e ^{x^{4} c o s (x)} ) ( 4 x ^{3} cos ( x ) - x ^{4} sin ( x ) )}{2 cos ( e ^{x^{4} c o s (x)} )}

Schritte zur Lösung

\frac{d}{d x} (cos (e^{x^{4} c o s (x)}))

Wende die Kettenregel an:

\frac{1}{2 cos ( e ^{x^{4} c o s (x)} )} \frac{d}{d x} (cos (e^{x^{4} c o s (x)}))

= \frac{1}{2 cos ( e ^{x^{4} c o s (x)} )} \frac{d}{d x} (cos (e^{x^{4} c o s (x)}))

\frac{d}{d x} (cos (e^{x^{4} c o s (x)})) = - sin (e^{x^{4} c o s (x)}) e^{x^{4} c o s (x)} (4 x^{3} cos (x) - x^{4} sin (x))

= \frac{1}{2 cos ( e ^{x^{4} c o s (x)} )} (- sin (e^{x^{4} c o s (x)}) e^{x^{4} c o s (x)} (4 x^{3} cos (x) - x^{4} sin (x)))

Vereinfache

\frac{1}{2 cos ( e ^{x^{4} c o s (x)} )} (- sin (e^{x^{4} c o s (x)}) e^{x^{4} c o s (x)} (4 x^{3} cos (x) - x^{4} sin (x))) : - \frac{e ^{x^{4} c o s (x)} sin ( e ^{x^{4} c o s (x)} ) ( 4 x ^{3} cos ( x ) - x ^{4} sin ( x ) )}{2 cos ( e ^{x^{4} c o s (x)} )}

= - \frac{e ^{x^{4} c o s (x)} sin ( e ^{x^{4} c o s (x)} ) ( 4 x ^{3} cos ( x ) - x ^{4} sin ( x ) )}{2 cos ( e ^{x^{4} c o s (x)} )}

x \to 0 lim (\frac{2 ∣ x ∣}{3 x})

d er i v a t i v e y = e^{9 - x}

\frac{\partial}{\partial x} (10 y + x)

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

d er i v a t i v e f (x) = \frac{x ^{2} - 1}{2}