derivative of-e^xcos(x)

解

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

- e^{x} cos (x) + e^{x} sin (x)

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (x)

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

\frac{d}{d x} (e^{x}) = e^{x}

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

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

簡素化

- (e^{x} cos (x) + (- sin (x)) e^{x}) : - e^{x} cos (x) + e^{x} sin (x)

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