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Beliebt Rechnen >

derivative 4^{3-x^2}

Lösung

ableitung von

4^{3 - x^{2}}

Lösung

- ln (2) \cdot 4^{- x^{2} + 4} x

Schritte zur Lösung

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

Wende Exponentenregel an:

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

4^{3 - x^{2}} = e^{(3 - x^{2}) l n (4)}

= \frac{d}{d x} (e^{(3 - x^{2}) l n (4)})

Wende die Kettenregel an:

e^{(3 - x^{2}) l n (4)} \frac{d}{d x} ((3 - x^{2}) ln (4))

= e^{(3 - x^{2}) l n (4)} \frac{d}{d x} ((3 - x^{2}) ln (4))

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

= e^{(3 - x^{2}) l n (4)} (- 4 ln (2) x)

Vereinfache

e^{(3 - x^{2}) l n (4)} (- 4 ln (2) x) : - ln (2) \cdot 4^{- x^{2} + 4} x

= - ln (2) \cdot 4^{- x^{2} + 4} x

Graph

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