derivative 2^{arctan(x)}

Lösung

ableitung von

2^{a r c t a n (x)}

\frac{ln ( 2 ) \cdot 2 ^{a r c t a n (x)}}{x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (2^{a r c t a n (x)})

Wende Exponentenregel an:

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

2^{a r c t a n (x)} = e^{a r c t a n (x) l n (2)}

= \frac{d}{d x} (e^{a r c t a n (x) l n (2)})

Wende die Kettenregel an:

e^{a r c t a n (x) l n (2)} \frac{d}{d x} (arctan (x) ln (2))

= e^{a r c t a n (x) l n (2)} \frac{d}{d x} (arctan (x) ln (2))

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

= e^{a r c t a n (x) l n (2)} \frac{ln ( 2 )}{x ^{2} + 1}

Vereinfache

e^{a r c t a n (x) l n (2)} \frac{ln ( 2 )}{x ^{2} + 1} : \frac{ln ( 2 ) \cdot 2 ^{a r c t a n (x)}}{x ^{2} + 1}

= \frac{ln ( 2 ) \cdot 2 ^{a r c t a n (x)}}{x ^{2} + 1}

\int (2 x - 3)^{2} d x

\frac{d}{d x} (x^{3} arctan (3 x))

d er i v a t i v e 3 (sin (x))^{x}

a re a x^{2} - 4, x = - 4, x = 3

d er i v a t i v e 3 e