(\partial)/(\partial x)(10^{x^2+x})

Lösung

\frac{\partial}{\partial x} (1 0^{x^{2} + x})

ln (10) \cdot 1 0^{x^{2} + x} (2 x + 1)

Schritte zur Lösung

\frac{\partial}{\partial x} (1 0^{x^{2} + x})

Wende Exponentenregel an:

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

1 0^{x^{2} + x} = e^{(x^{2} + x) l n (10)}

= \frac{\partial}{\partial x} (e^{(x^{2} + x) l n (10)})

Wende die Kettenregel an:

e^{(x^{2} + x) l n (10)} \frac{\partial}{\partial x} ((x^{2} + x) ln (10))

= e^{(x^{2} + x) l n (10)} \frac{\partial}{\partial x} ((x^{2} + x) ln (10))

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

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

e^{(x^{2} + x) l n (10)} = 1 0^{x^{2} + x}

= ln (10) \cdot 1 0^{x^{2} + x} (2 x + 1)

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