derivative y=x^{6x}

Lösung

ableitung von

y = x^{6 x}

6 x^{6 x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (x^{6 x})

Wende Exponentenregel an:

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

x^{6 x} = e^{6 x l n (x)}

= \frac{d}{d x} (e^{6 x l n (x)})

Wende die Kettenregel an:

e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

= e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

\frac{d}{d x} (6 x ln (x)) = 6 (ln (x) + 1)

= e^{6 x l n (x)} \cdot 6 (ln (x) + 1)

e^{6 x l n (x)} = x^{6 x}

= 6 x^{6 x} (ln (x) + 1)

\int 8 sin (2) (x) cos (3) (x) d x

x \to 0 lim (\frac{1 - cos ( 2 x )}{x})

x \to 1 + lim (\frac{1}{x - 1} - \frac{1}{ln ( x )})

\int \frac{( e ^{6 x} )}{e ^{6 x} + 1} d x

\frac{d y}{d t} = (t y)^{2}