derivative of sin(4x+7x^4+e^{1-x^2})

解

\frac{d}{d x} (sin (4 x + 7 x^{4}) + e^{1 - x^{2}})

cos (4 x + 7 x^{4}) (4 + 28 x^{3}) - 2 e^{1 - x^{2}} x

解答ステップ

\frac{d}{d x} (sin (4 x + 7 x^{4}) + e^{1 - x^{2}})

和/差の法則を適用:

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

= \frac{d}{d x} (sin (4 x + 7 x^{4})) + \frac{d}{d x} (e^{1 - x^{2}})

\frac{d}{d x} (sin (4 x + 7 x^{4})) = cos (4 x + 7 x^{4}) (4 + 28 x^{3})

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

= cos (4 x + 7 x^{4}) (4 + 28 x^{3}) - 2 e^{1 - x^{2}} x