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Beliebt Rechnen >

derivative y=(sqrt(x))^x

Lösung

ableitung von

y = (x)^{x}

Lösung

(x)^{x} (ln (x) + \frac{1}{2})

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

(x)^{x} = e^{x l n (x)}

= \frac{d}{d x} (e^{x l n (x)})

Wende die Kettenregel an:

e^{x l n (x)} \frac{d}{d x} (x ln (x))

= e^{x l n (x)} \frac{d}{d x} (x ln (x))

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

= e^{x l n (x)} (ln (x) + \frac{1}{2})

e^{x l n (x)} = (x)^{x}

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

Graph

Beliebte Beispiele

f (x) = 7 sin (x)

derivative of (-2/x)

\frac{d}{d x} (\frac{- 2}{x})

integral of x/(sqrt(x^2-16))

\int \frac{x}{x ^{2} - 16} d x

derivative f(x)=x(x^2+1)

d er i v a t i v e f (x) = x (x^{2} + 1)

derivative (x/(x-1))^x

d er i v a t i v e (\frac{x}{x - 1})^{x}