derivative f(x)=x^{2x}

Lösung

ableitung von

f (x) = x^{2 x}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

\int \frac{1}{cot ( y )} d y

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

\int \frac{x ^{2} - 3 x - 7}{( 2 x + 3 ) ( x + 1 ) ^{2}} d x

\frac{d}{d x} (\frac{x ^{2}}{x ^{4} + 1})

\frac{d y}{d x} = 2 y - 1