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人気のある微分積分 >

derivative of ln(x^3+6x^2)

解

\frac{d}{d x} (ln (x^{3} + 6 x^{2}))

解

\frac{3 ( x + 4 )}{x ( x + 6 )}

解答ステップ

\frac{d}{d x} (ln (x^{3} + 6 x^{2}))

連鎖法則を適用:

\frac{1}{x ^{3} + 6 x ^{2}} \frac{d}{d x} (x^{3} + 6 x^{2})

= \frac{1}{x ^{3} + 6 x ^{2}} \frac{d}{d x} (x^{3} + 6 x^{2})

\frac{d}{d x} (x^{3} + 6 x^{2}) = 3 x^{2} + 12 x

= \frac{1}{x ^{3} + 6 x ^{2}} (3 x^{2} + 12 x)

簡素化

\frac{1}{x ^{3} + 6 x ^{2}} (3 x^{2} + 12 x) : \frac{3 ( x + 4 )}{x ( x + 6 )}

= \frac{3 ( x + 4 )}{x ( x + 6 )}

グラフ

人気の例

(\partial)/(\partial x)((w^Te^{-w^Tx})/((1+e^{-w^Tx))^2})

\frac{\partial}{\partial x} (\frac{w ^{T} e ^{- w^{T} x}}{( 1 + e ^{- w^{T} x} ) ^{2}})

integral of 1/(x^3sqrt(x^2-64))

\int \frac{1}{x ^{3} x ^{2} - 64} d x

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