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人気のある微分積分 >

derivative y= 7/(ln(x))

解

導関数

y = \frac{7}{ln ( x )}

解

- \frac{7}{x ln ^{2} ( x )}

解答ステップ

\frac{d}{d x} (\frac{7}{ln ( x )})

定数を除去:

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

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

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= 7 \frac{d}{d x} (ln^{- 1} (x))

連鎖法則を適用:

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

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

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

= 7 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

簡素化

7 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{7}{x ln ^{2} ( x )}

= - \frac{7}{x ln ^{2} ( x )}

グラフ

人気の例

derivative of (5x/6)

\frac{d}{d x} (\frac{5 x}{6})

limit as x approaches 9-of 1/(x-9)

x \to 9 - lim (\frac{1}{x - 9})

limit as x approaches 0+of x[ln(x)]^2

x \to 0 + lim (x [ln (x)]^{2})

derivative of 2^{5x}3^{4x^2}

\frac{d}{d x} (2^{5 x} 3^{4 x^{2}})

(dy)/(dx)=(x-4)/(y+5)

\frac{d y}{d x} = \frac{x - 4}{y + 5}