derivative of e^{e^{e^{e^x}}}

Lösung

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

e^{e^{e^{e^{x}}} + e^{e^{x}} + e^{x} + x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (e^{e^{e^{x}}}) = e^{e^{e^{x}} + e^{x} + x}

= e^{e^{e^{e^{x}}}} e^{e^{e^{x}} + e^{x} + x}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

e^{e^{e^{e^{x}}}} e^{e^{e^{x}} + e^{x} + x} = e^{e^{e^{e^{x}}} + e^{e^{x}} + e^{x} + x}

= e^{e^{e^{e^{x}}} + e^{e^{x}} + e^{x} + x}

\int r^{2} d r

x \to 0 lim (\frac{7 x}{cot ( x )})

\frac{\partial}{\partial s} (s sin (t))

\int 2 sin (x) 3 1 + cos (x) d x

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