derivative of (e^{x^2}/(cos(3x)))

解

\frac{d}{d x} (\frac{e ^{x^{2}}}{cos ( 3 x )})

e^{x^{2}} \cdot 2 x sec (3 x) + sec (3 x) tan (3 x) \cdot 3 e^{x^{2}}

解答ステップ

\frac{d}{d x} (\frac{e ^{x^{2}}}{cos ( 3 x )})

簡素化

\frac{e ^{x^{2}}}{cos ( 3 x )} : e^{x^{2}} sec (3 x)

= \frac{d}{d x} (e^{x^{2}} sec (3 x))

積の法則を適用:

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

f = e^{x^{2}}, g = sec (3 x)

= \frac{d}{d x} (e^{x^{2}}) sec (3 x) + \frac{d}{d x} (sec (3 x)) e^{x^{2}}

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

\frac{d}{d x} (sec (3 x)) = sec (3 x) tan (3 x) \cdot 3

= e^{x^{2}} \cdot 2 x sec (3 x) + sec (3 x) tan (3 x) \cdot 3 e^{x^{2}}