derivative of 8^{4-x^2}

Lösung

\frac{d}{d x} (8^{4 - x^{2}})

- 3 ln (2) \cdot 2^{- 3 x^{2} + 13} x

Schritte zur Lösung

\frac{d}{d x} (8^{4 - x^{2}})

Wende Exponentenregel an:

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

8^{4 - x^{2}} = e^{(4 - x^{2}) l n (8)}

= \frac{d}{d x} (e^{(4 - x^{2}) l n (8)})

Wende die Kettenregel an:

e^{(4 - x^{2}) l n (8)} \frac{d}{d x} ((4 - x^{2}) ln (8))

= e^{(4 - x^{2}) l n (8)} \frac{d}{d x} ((4 - x^{2}) ln (8))

\frac{d}{d x} ((4 - x^{2}) ln (8)) = - 6 ln (2) x

= e^{(4 - x^{2}) l n (8)} (- 6 ln (2) x)

Vereinfache

e^{(4 - x^{2}) l n (8)} (- 6 ln (2) x) : - 3 ln (2) \cdot 2^{- 3 x^{2} + 13} x

= - 3 ln (2) \cdot 2^{- 3 x^{2} + 13} x

s l o p e (x^{2} - 35)^{6}

\frac{d}{d x} (\frac{1}{sin ( x ) + cos ( x )})

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\int \frac{29}{( x + 1 ) ( x ^{2} + x )} d x

d er i v a t i v e y = \frac{e ^{x}}{9 x ^{2}}