derivative of e^{-3x^4}*ln(7x^2)

解

\frac{d}{d x} (e^{- 3 x^{4}} \cdot ln (7 x^{2}))

- 12 e^{- 3 x^{4}} x^{3} ln (7 x^{2}) + \frac{2 e ^{- 3 x^{4}}}{x}

解答ステップ

\frac{d}{d x} (e^{- 3 x^{4}} ln (7 x^{2}))

積の法則を適用:

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

f = e^{- 3 x^{4}}, g = ln (7 x^{2})

= \frac{d}{d x} (e^{- 3 x^{4}}) ln (7 x^{2}) + \frac{d}{d x} (ln (7 x^{2})) e^{- 3 x^{4}}

\frac{d}{d x} (e^{- 3 x^{4}}) = - 12 e^{- 3 x^{4}} x^{3}

\frac{d}{d x} (ln (7 x^{2})) = \frac{2}{x}

= (- 12 e^{- 3 x^{4}} x^{3}) ln (7 x^{2}) + \frac{2}{x} e^{- 3 x^{4}}

簡素化

(- 12 e^{- 3 x^{4}} x^{3}) ln (7 x^{2}) + \frac{2}{x} e^{- 3 x^{4}} : - 12 e^{- 3 x^{4}} x^{3} ln (7 x^{2}) + \frac{2 e ^{- 3 x^{4}}}{x}

= - 12 e^{- 3 x^{4}} x^{3} ln (7 x^{2}) + \frac{2 e ^{- 3 x^{4}}}{x}