derivative of 8^{-3x^2}

Lösung

\frac{d}{d x} (8^{- 3 x^{2}})

- 9 ln (2) \cdot 2^{- 9 x^{2} + 1} x

Schritte zur Lösung

\frac{d}{d x} (8^{- 3 x^{2}})

Vereinfache

8^{- 3 x^{2}} : 51 2^{- x^{2}}

= \frac{d}{d x} (51 2^{- x^{2}})

Wende Exponentenregel an:

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

51 2^{- x^{2}} = e^{(- x^{2}) l n (512)}

= \frac{d}{d x} (e^{(- x^{2}) l n (512)})

Wende die Kettenregel an:

e^{(- x^{2}) l n (512)} \frac{d}{d x} ((- x^{2}) ln (512))

= e^{(- x^{2}) l n (512)} \frac{d}{d x} ((- x^{2}) ln (512))

\frac{d}{d x} ((- x^{2}) ln (512)) = - 18 ln (2) x

= e^{(- x^{2}) l n (512)} (- 18 ln (2) x)

Vereinfache

e^{(- x^{2}) l n (512)} (- 18 ln (2) x) : - 9 ln (2) \cdot 2^{- 9 x^{2} + 1} x

= - 9 ln (2) \cdot 2^{- 9 x^{2} + 1} x

\int \frac{3}{4 2 x + 5} d x

x \to 5 + lim (- ln (5 - x))

\frac{\partial}{\partial x} (x^{3} + 3 x y^{2})

s l o p e (7, 3), (2, - 3)

a re a 4 x - x^{2}, x