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人気のある微分積分 >

derivative x^2log_{10}(1/x)

解

導関数

x^{2} lo g_{10} (\frac{1}{x})

解

- \frac{x + 2 x ln ( x )}{ln ( 10 )}

解答ステップ

\frac{d}{d x} (x^{2} lo g_{10} (\frac{1}{x}))

簡素化

x^{2} lo g_{10} (\frac{1}{x}) : - x^{2} lo g_{10} (x)

= \frac{d}{d x} (- x^{2} lo g_{10} (x))

定数を除去:

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

= - \frac{d}{d x} (x^{2} lo g_{10} (x))

積の法則を適用:

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

f = x^{2}, g = lo g_{10} (x)

= - (\frac{d}{d x} (x^{2}) lo g_{10} (x) + \frac{d}{d x} (lo g_{10} (x)) x^{2})

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

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

= - (2 x lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{2})

簡素化

- (2 x lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{2}) : - \frac{x + 2 x ln ( x )}{ln ( 10 )}

= - \frac{x + 2 x ln ( x )}{ln ( 10 )}

グラフ

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