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Beliebt Rechnen >

derivative of 4^{9-x^2}

Lösung

\frac{d}{d x} (4^{9 - x^{2}})

Lösung

- ln (2) \cdot 4^{- x^{2} + 10} x

Schritte zur Lösung

\frac{d}{d x} (4^{9 - x^{2}})

Wende Exponentenregel an:

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

4^{9 - x^{2}} = e^{(9 - x^{2}) l n (4)}

= \frac{d}{d x} (e^{(9 - x^{2}) l n (4)})

Wende die Kettenregel an:

e^{(9 - x^{2}) l n (4)} \frac{d}{d x} ((9 - x^{2}) ln (4))

= e^{(9 - x^{2}) l n (4)} \frac{d}{d x} ((9 - x^{2}) ln (4))

\frac{d}{d x} ((9 - x^{2}) ln (4)) = - 4 ln (2) x

= e^{(9 - x^{2}) l n (4)} (- 4 ln (2) x)

Vereinfache

e^{(9 - x^{2}) l n (4)} (- 4 ln (2) x) : - ln (2) \cdot 4^{- x^{2} + 10} x

= - ln (2) \cdot 4^{- x^{2} + 10} x

Graph

Beliebte Beispiele

integral of 1/(1+y^2)

\int \frac{1}{1 + y ^{2}} d y

limit as x approaches 0 of (x^2-4)/(x-2)

x \to 0 lim (\frac{x ^{2} - 4}{x - 2})

limit as x approaches 0 of sqrt(x)+x+x^2

x \to 0 lim (x + x + x^{2})

\frac{d y}{d x} = 9 x^{2}

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