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人気のある微分積分 >

derivative f(x)=ln(4-x^6)

解

導関数

f (x) = ln (4 - x^{6})

解

- \frac{6 x ^{5}}{4 - x ^{6}}

解答ステップ

\frac{d}{d x} (ln (4 - x^{6}))

連鎖法則を適用:

\frac{1}{4 - x ^{6}} \frac{d}{d x} (4 - x^{6})

= \frac{1}{4 - x ^{6}} \frac{d}{d x} (4 - x^{6})

\frac{d}{d x} (4 - x^{6}) = - 6 x^{5}

= \frac{1}{4 - x ^{6}} (- 6 x^{5})

簡素化

\frac{1}{4 - x ^{6}} (- 6 x^{5}) : - \frac{6 x ^{5}}{4 - x ^{6}}

= - \frac{6 x ^{5}}{4 - x ^{6}}

グラフ

人気の例

integral of xsin((npix)/(20))

\int x sin (\frac{nπ x}{20}) d x

limit as x approaches 2-of (x^2-4)/(x-2)

x \to 2 - lim (\frac{x ^{2} - 4}{x - 2})

derivative of (4x(2x^2+3)/((1-2x^2)^3))

\frac{d}{d x} (\frac{4 x ( 2 x ^{2} + 3 )}{( 1 - 2 x ^{2} ) ^{3}})

integral of (3x+2)/((x+5)(x-2))

\int \frac{3 x + 2}{( x + 5 ) ( x - 2 )} d x

limit as s approaches-8 of 4(s)-2

s \to - 8 lim (4 (s) - 2)