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人気のある微分積分 >

derivative of ln(1+x^3)

解

\frac{d}{d x} (ln (1 + x^{3}))

解

\frac{3 x ^{2}}{1 + x ^{3}}

解答ステップ

\frac{d}{d x} (ln (1 + x^{3}))

連鎖法則を適用:

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

= \frac{1}{1 + x ^{3}} \frac{d}{d x} (1 + x^{3})

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

= \frac{1}{1 + x ^{3}} \cdot 3 x^{2}

簡素化

\frac{1}{1 + x ^{3}} \cdot 3 x^{2} : \frac{3 x ^{2}}{1 + x ^{3}}

= \frac{3 x ^{2}}{1 + x ^{3}}

グラフ

人気の例

tangent y=x^3-2x+1,(0,1)

t an g e n t y = x^{3} - 2 x + 1, (0, 1)

integral of x/((x^2+1)^{3/2)}

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

integral from 1 to 2 of (15)/(x^3+4x)

\int_{1}^{2} \frac{15}{x ^{3} + 4 x} d x

(\partial)/(\partial y)((x+4y+3z)^{3/2})

\frac{\partial}{\partial y} ((x + 4 y + 3 z)^{\frac{3}{2}})

derivative y=3x+7

d er i v a t i v e y = 3 x + 7