derivative f(x)=e^xsin^2(x)

解

導関数

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

e^{x} sin^{2} (x) + sin (2 x) e^{x}

解答ステップ

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

積の法則を適用:

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

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

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

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

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

= e^{x} sin^{2} (x) + sin (2 x) e^{x}