derivative of-(cos^2(x+cos^2(y))2)

解

\frac{d}{d x} (- (cos^{2} (x) + cos^{2} (y)) 2)

- 2 (- sin (2 x) - 2 cos (y) sin (y) \frac{d y}{d x})

解答ステップ

\frac{d}{d x} (- (cos^{2} (x) + cos^{2} (y)) \cdot 2)

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \frac{d}{d x} (cos^{2} (x) + cos^{2} (y))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - 2 (\frac{d}{d x} (cos^{2} (x)) + \frac{d}{d x} (cos^{2} (y)))

\frac{d}{d x} (cos^{2} (x)) = - sin (2 x)

\frac{d}{d x} (cos^{2} (y)) = - 2 cos (y) sin (y) \frac{d y}{d x}

= - 2 (- sin (2 x) - 2 cos (y) sin (y) \frac{d y}{d x})