derivative nlog_{10}(n)

解

導関数

n lo g_{10} (n)

lo g_{10} (n) + \frac{1}{ln ( 10 )}

解答ステップ

\frac{d}{d n} (n lo g_{10} (n))

積の法則を適用:

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

f = n, g = lo g_{10} (n)

= \frac{d n}{d n} lo g_{10} (n) + \frac{d}{d n} (lo g_{10} (n)) n

\frac{d n}{d n} = 1

\frac{d}{d n} (lo g_{10} (n)) = \frac{1}{n ln ( 10 )}

= 1 \cdot lo g_{10} (n) + \frac{1}{n ln ( 10 )} n

簡素化

1 \cdot lo g_{10} (n) + \frac{1}{n ln ( 10 )} n : lo g_{10} (n) + \frac{1}{ln ( 10 )}

= lo g_{10} (n) + \frac{1}{ln ( 10 )}