derivative 2xlog_{7}(sqrt(x))

解

導関数

2 x lo g_{7} (x)

2 lo g_{7} (x) + \frac{1}{ln ( 7 )}

解答ステップ

\frac{d}{d x} (2 x lo g_{7} (x))

定数を除去:

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

= 2 \frac{d}{d x} (x lo g_{7} (x))

積の法則を適用:

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

f = x, g = lo g_{7} (x)

= 2 (\frac{d x}{d x} lo g_{7} (x) + \frac{d}{d x} (lo g_{7} (x)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (lo g_{7} (x)) = \frac{1}{2 ln ( 7 ) x}

= 2 (1 \cdot lo g_{7} (x) + \frac{1}{2 ln ( 7 ) x} x)

簡素化

2 (1 \cdot lo g_{7} (x) + \frac{1}{2 ln ( 7 ) x} x) : 2 lo g_{7} (x) + \frac{1}{ln ( 7 )}

= 2 lo g_{7} (x) + \frac{1}{ln ( 7 )}