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Beliebt Rechnen >

derivative 2^{8-x^2}

Lösung

ableitung von

2^{8 - x^{2}}

Lösung

- ln (2) \cdot 2^{- x^{2} + 9} x

Schritte zur Lösung

\frac{d}{d x} (2^{8 - x^{2}})

Wende Exponentenregel an:

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

2^{8 - x^{2}} = e^{(8 - x^{2}) l n (2)}

= \frac{d}{d x} (e^{(8 - x^{2}) l n (2)})

Wende die Kettenregel an:

e^{(8 - x^{2}) l n (2)} \frac{d}{d x} ((8 - x^{2}) ln (2))

= e^{(8 - x^{2}) l n (2)} \frac{d}{d x} ((8 - x^{2}) ln (2))

\frac{d}{d x} ((8 - x^{2}) ln (2)) = - 2 ln (2) x

= e^{(8 - x^{2}) l n (2)} (- 2 ln (2) x)

Vereinfache

e^{(8 - x^{2}) l n (2)} (- 2 ln (2) x) : - ln (2) \cdot 2^{- x^{2} + 9} x

= - ln (2) \cdot 2^{- x^{2} + 9} x

Graph

Beliebte Beispiele

integral of 1/(4x^2+2)

\int \frac{1}{4 x ^{2} + 2} d x

sum from n=0 to infinity of ((n^n))/(n!)

n = 0 \sum \infty \frac{( n ^{n} )}{n !}

integral of 1/z

\int \frac{1}{z} d z

derivative of 3x^3-x^2+1

\frac{d}{d x} (3 x^{3} - x^{2} + 1)

slopeintercept (-8.2)(-10.5)

s l o p e in t erce pt (- 8.2) (- 10.5)