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人気のある微分積分 >

derivative of ln(x^x)

解

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

解

ln (x) + 1

解答ステップ

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

連鎖法則を適用:

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

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

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

= \frac{1}{x ^{x}} x^{x} (ln (x) + 1)

簡素化

\frac{1}{x ^{x}} x^{x} (ln (x) + 1) : ln (x) + 1

= ln (x) + 1

グラフ

人気の例

integral of 4xe^{-2x^2}

\int 4 x e^{- 2 x^{2}} d x

derivative of (cos(x+2)^3)

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

integral of (4x)/((x^2+6)^2)

\int \frac{4 x}{( x ^{2} + 6 ) ^{2}} d x

(dy)/(dx)=(x+y)^2-1

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

derivative of-2/(9x^{5/3})

\frac{d}{d x} (- \frac{2}{9 x ^{\frac{5}{3}}})