derivative of (x^2^{2x})

Lösung

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

2 x^{4 x} (2 ln (x) + 2)

Schritte zur Lösung

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

Wende Exponentenregel an:

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

(x^{2})^{2 x} = e^{2 x l n (x^{2})}

= \frac{d}{d x} (e^{2 x l n (x^{2})})

Wende die Kettenregel an:

e^{2 x l n (x^{2})} \frac{d}{d x} (2 x ln (x^{2}))

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

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

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

Vereinfache

e^{2 x l n (x^{2})} \cdot 2 (ln (x^{2}) + 2) : 2 x^{4 x} (2 ln (x) + 2)

= 2 x^{4 x} (2 ln (x) + 2)

in v erse l a pl a ce \frac{8 s ^{2} - 4 s + 12}{s ( s ^{2} + 4 )}

t an g e n t f (x) = x, at x = \frac{49}{121}

\frac{d ^{4}}{d x ^{4}} (2 e^{x^{2}})

\frac{\partial}{\partial y} (y + x y)

x \to - 4 lim (\frac{x ^{2} + 3 x - 4}{x + 4})