derivative 2^{x^2}

Lösung

ableitung von

2^{x^{2}}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

= e^{x^{2} l n (2)} \cdot 2 ln (2) x

Vereinfache

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

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

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

\int \frac{1}{x ^{2} + 8 x + 25} d x

x y^{^{'}} + (1 - x) y = 2 x e^{x}

x \to 4 - lim (\frac{5}{x - 4})

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