(\partial)/(\partial x)((2x)^x)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

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t an g e n t f (x) = 2 x^{2} + 5 x - 3

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