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

解

導関数

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)} )}

解答ステップ

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

連鎖法則を適用:

\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)))

簡素化

\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)} )}