derivative 3^{x^2}

Lösung

ableitung von

3^{x^{2}}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

y^{^{'}} = \frac{3 sec ( y )}{( x - 4 ) ^{2}}

\int_{1}^{\infty} \frac{x}{x ^{2} + 4} d x

\frac{d}{d x} (\frac{3 π}{2})

x \to 0 lim (tan^{x} (9 x))

\frac{\partial}{\partial x} (x^{3} - 3 x y + y^{3} - 2)