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Beliebt Rechnen >

derivative of log_{e}(x^x)

Lösung

\frac{d}{d x} (lo g_{e} (x^{x}))

Lösung

ln (x) + 1

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (x^{x}))

Vereinfache

lo g_{e} (x^{x}) : ln (x^{x})

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

Wende die Kettenregel an:

\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)

Vereinfache

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

= ln (x) + 1

Graph

Beliebte Beispiele

derivative cos^2(θ)

d er i v a t i v e cos^{2} (θ)

(dy)/(dx)=y(950-y)

\frac{d y}{d x} = y (950 - y)

integral of 7/(sqrt(x+7)+\sqrt{x)}

\int \frac{7}{x + 7 + x} d x

derivative of (x^3y-xy^3/(x^2+y^2))

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

integral of (8x)/(x^2+4)

\int \frac{8 x}{x ^{2} + 4} d x