derivative of e^{x^2-4}+2x+9

解

\frac{d}{d x} (e^{x^{2} - 4} + 2 x + 9)

2 e^{x^{2} - 4} x + 2

解答ステップ

\frac{d}{d x} (e^{x^{2} - 4} + 2 x + 9)

和/差の法則を適用:

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

= \frac{d}{d x} (e^{x^{2} - 4}) + \frac{d}{d x} (2 x) + \frac{d}{d x} (9)

\frac{d}{d x} (e^{x^{2} - 4}) = e^{x^{2} - 4} \cdot 2 x

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

\frac{d}{d x} (9) = 0

= e^{x^{2} - 4} \cdot 2 x + 2 + 0

簡素化

= 2 e^{x^{2} - 4} x + 2