derivative 2^xln^2(x)

解

導関数

2^{x} ln^{2} (x)

ln (2) \cdot 2^{x} ln^{2} (x) + \frac{2 ^{1 + x} ln ( x )}{x}

解答ステップ

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

積の法則を適用:

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

f = 2^{x}, g = ln^{2} (x)

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

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

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

= 2^{x} ln (2) ln^{2} (x) + \frac{2 ln ( x )}{x} \cdot 2^{x}

\frac{2 ln ( x )}{x} \cdot 2^{x} = \frac{2 ^{1 + x} ln ( x )}{x}

= ln (2) \cdot 2^{x} ln^{2} (x) + \frac{2 ^{1 + x} ln ( x )}{x}