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Beliebt Rechnen >

(\partial)/(\partial x)(2^{x^2-y^5})

Lösung

\frac{\partial}{\partial x} (2^{x^{2} - y^{5}})

Lösung

ln (2) \cdot 2^{x^{2} - y^{5} + 1} x

Schritte zur Lösung

\frac{\partial}{\partial x} (2^{x^{2} - y^{5}})

Behandle

y

als Konstante

Wende Exponentenregel an:

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

2^{x^{2} - y^{5}} = e^{(x^{2} - y^{5}) l n (2)}

= \frac{\partial}{\partial x} (e^{(x^{2} - y^{5}) l n (2)})

Wende die Kettenregel an:

e^{(x^{2} - y^{5}) l n (2)} \frac{\partial}{\partial x} ((x^{2} - y^{5}) ln (2))

= e^{(x^{2} - y^{5}) l n (2)} \frac{\partial}{\partial x} ((x^{2} - y^{5}) ln (2))

\frac{\partial}{\partial x} ((x^{2} - y^{5}) ln (2)) = 2 ln (2) x

= e^{(x^{2} - y^{5}) l n (2)} \cdot 2 ln (2) x

Vereinfache

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

= ln (2) \cdot 2^{x^{2} - y^{5} + 1} x

Beliebte Beispiele

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