derivative y=3^{cos(2x)}+e^3

解

導関数

y = 3^{c o s (2 x)} + e^{3}

- 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

解答ステップ

\frac{d}{d x} (3^{c o s (2 x)} + e^{3})

和/差の法則を適用:

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

= \frac{d}{d x} (3^{c o s (2 x)}) + \frac{d}{d x} (e^{3})

\frac{d}{d x} (3^{c o s (2 x)}) = - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

\frac{d}{d x} (e^{3}) = 0

= - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x) + 0

簡素化

= - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)