derivative 5^{3^{x^2}}

Lösung

ableitung von

5^{3^{x^{2}}}

2 ln (5) ln (3) \cdot 5^{3^{x^{2}}} \cdot 3^{x^{2}} x

Schritte zur Lösung

\frac{d}{d x} (5^{3^{x^{2}}})

Wende Exponentenregel an:

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

5^{3^{x^{2}}} = e^{3^{x^{2}} l n (5)}

= \frac{d}{d x} (e^{3^{x^{2}} l n (5)})

Wende die Kettenregel an:

e^{3^{x^{2}} l n (5)} \frac{d}{d x} (3^{x^{2}} ln (5))

= e^{3^{x^{2}} l n (5)} \frac{d}{d x} (3^{x^{2}} ln (5))

\frac{d}{d x} (3^{x^{2}} ln (5)) = 2 ln (5) ln (3) \cdot 3^{x^{2}} x

= e^{3^{x^{2}} l n (5)} \cdot 2 ln (5) ln (3) \cdot 3^{x^{2}} x

e^{3^{x^{2}} l n (5)} = 5^{3^{x^{2}}}

= 2 ln (5) ln (3) \cdot 5^{3^{x^{2}}} \cdot 3^{x^{2}} x

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

\int \frac{e ^{3 x}}{x ^{\frac{2}{3}}} d x

t an g e n t f (x) = \frac{3 x}{x + 1}, at x = 2

d er i v a t i v e \frac{4 x}{x ^{2} + 1}

\frac{d}{d x} (\frac{( x + a ) ^{3}}{b} - c)