derivative f(x)=3e^xsqrt(x)

解

導関数

f (x) = 3 e^{x} x

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

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

積の法則を適用:

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

f = e^{x}, g = x

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

= 3 (e^{x} x + \frac{1}{2 x} e^{x})

\frac{1}{2 x} e^{x} = \frac{e ^{x}}{2 x}

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