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

解

\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)} )}

解答ステップ

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

連鎖法則を適用:

\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)))

簡素化

\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)} )}