derivative 6^{2^{x^2}}

Lösung

ableitung von

6^{2^{x^{2}}}

ln (6) ln (2) \cdot 3^{2^{x^{2}}} \cdot 2^{2^{x^{2}} + x^{2} + 1} x

Schritte zur Lösung

\frac{d}{d x} (6^{2^{x^{2}}})

Wende Exponentenregel an:

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

6^{2^{x^{2}}} = e^{2^{x^{2}} l n (6)}

= \frac{d}{d x} (e^{2^{x^{2}} l n (6)})

Wende die Kettenregel an:

e^{2^{x^{2}} l n (6)} \frac{d}{d x} (2^{x^{2}} ln (6))

= e^{2^{x^{2}} l n (6)} \frac{d}{d x} (2^{x^{2}} ln (6))

\frac{d}{d x} (2^{x^{2}} ln (6)) = ln (6) ln (2) \cdot 2^{x^{2} + 1} x

= e^{2^{x^{2}} l n (6)} ln (6) ln (2) \cdot 2^{x^{2} + 1} x

Vereinfache

e^{2^{x^{2}} l n (6)} ln (6) ln (2) \cdot 2^{x^{2} + 1} x : ln (6) ln (2) \cdot 3^{2^{x^{2}}} \cdot 2^{2^{x^{2}} + x^{2} + 1} x

= ln (6) ln (2) \cdot 3^{2^{x^{2}}} \cdot 2^{2^{x^{2}} + x^{2} + 1} x

\int_{0}^{1} \frac{2 x}{( x ^{2} + 1 ) ^{3}} d x

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

\frac{d}{d y} (\frac{3 x}{2 y})

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

a re a y = - x, y = 2 - x, y = 0