derivative of x^{x^x}

Lösung

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

x^{x^{x}} (x^{x} ln (x) (ln (x) + 1) + x^{x - 1})

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

= e^{x^{x} l n (x)} (x^{x} ln (x) (ln (x) + 1) + x^{x - 1})

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

= x^{x^{x}} (x^{x} ln (x) (ln (x) + 1) + x^{x - 1})

\int \frac{2 x}{3 x ^{2} - 4} d x

d er i v a t i v e \frac{3}{5 + x ^{2}}

t a y l or e^{3 x^{3}}

n or ma l f (x) = x \cdot 5^{x}, at x = 1

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{3} t