derivative of e^{x^2}sin(x)

解

\frac{d}{d x} (e^{x^{2}} sin (x))

e^{x^{2}} \cdot 2 x sin (x) + cos (x) e^{x^{2}}

解答ステップ

\frac{d}{d x} (e^{x^{2}} sin (x))

積の法則を適用:

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

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

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= e^{x^{2}} \cdot 2 x sin (x) + cos (x) e^{x^{2}}