derivative f(x)=2^{x^2}

Lösung

ableitung von

f (x) = 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_{0}^{4} π (\frac{y ^{2}}{2})^{2} d y

\int_{3}^{5} \frac{1}{4 + ( x - 3 ) ^{2}} d x

y^{^{'}} + 3 y = e^{x} y^{2}

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

9 y^{^{''}} + y = 0