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人気のある微分積分 >

derivative log_{10}((x+1)/x)

解

導関数

lo g_{10} (\frac{x + 1}{x})

解

- \frac{1}{ln ( 10 ) x ( x + 1 )}

解答ステップ

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

対数の規則を適用する:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

定数を除去:

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

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

連鎖法則を適用:

\frac{1}{\frac{x + 1}{x}} \frac{d}{d x} (\frac{x + 1}{x})

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

\frac{d}{d x} (\frac{x + 1}{x}) = - \frac{1}{x ^{2}}

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

簡素化

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

= - \frac{1}{ln ( 10 ) x ( x + 1 )}

グラフ

人気の例

derivative (x^2)^x

d er i v a t i v e (x^{2})^{x}

derivative ((x-1)/x)^2

d er i v a t i v e (\frac{x - 1}{x})^{2}

derivative of 1.2*sin(2*x-0.8*t+10)

\frac{d}{d x} (1.2 \cdot sin (2 \cdot x - 0.8 \cdot t + 10))

derivative cot^3(x)

d er i v a t i v e cot^{3} (x)

derivative y=(4-3x)^9

d er i v a t i v e y = (4 - 3 x)^{9}