derivative e^{-(x+2)}-sin(x^2)+1

解

導関数

e^{- (x + 2)} - sin (x^{2}) + 1

- 2 x cos (x^{2}) - e^{- x - 2}

解答ステップ

\frac{d}{d x} (e^{- (x + 2)} - sin (x^{2}) + 1)

簡素化

e^{- (x + 2)} - sin (x^{2}) + 1 : e^{- x - 2} - sin (x^{2}) + 1

= \frac{d}{d x} (e^{- x - 2} - sin (x^{2}) + 1)

和/差の法則を適用:

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

= \frac{d}{d x} (e^{- x - 2}) - \frac{d}{d x} (sin (x^{2})) + \frac{d}{d x} (1)

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

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

\frac{d}{d x} (1) = 0

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

簡素化

= - 2 x cos (x^{2}) - e^{- x - 2}