derivative of 5x^{2x}

Lösung

\frac{d}{d x} (5 x^{2 x})

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

Schritte zur Lösung

\frac{d}{d x} (5 x^{2 x})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \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)}

= 5 \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)

= 5 e^{2 x l n (x)} \cdot 2 (ln (x) + 1)

Vereinfache

5 e^{2 x l n (x)} \cdot 2 (ln (x) + 1) : 10 x^{2 x} (ln (x) + 1)

= 10 x^{2 x} (ln (x) + 1)

\int 2 x \cdot e^{2 x} d x

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

\frac{d}{d x} (4 x + 8 x^{\frac{3}{8}})

\frac{d}{d x} \frac{( x ^{2} - 4 ) ^{3}}{36}

x \to 1 + lim (\frac{1}{x ^{3}})