derivative of 4^{-x^2}

Lösung

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

- ln (2) \cdot 4^{- x^{2} + 1} x

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

e^{(- x^{2}) l n (4)} (- 4 ln (2) x) : - ln (2) \cdot 4^{- x^{2} + 1} x

= - ln (2) \cdot 4^{- x^{2} + 1} x

\frac{d}{d x} (4 cos (2 x))

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

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

\int x cos (3 x) d x

\frac{d}{d t} (v (t) e^{0.1 t})