derivative of (cos(x)/(e^{2x)}-2)

解

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

- \frac{sin ( x ) + 2 cos ( x )}{e ^{2 x}}

解答ステップ

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (2) = 0

= - \frac{sin ( x ) + 2 cos ( x )}{e ^{2 x}} - 0

簡素化

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