(\partial)/(\partial x)(5^{x^2})

Lösung

\frac{\partial}{\partial x} (5^{x^{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (5^{x^{2}})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (x^{2} ln (5)) = 2 ln (5) x

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

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

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

\int \frac{4}{e ^{x}} d x

\int e^{- 11 x} d x

in v erse l a pl a ce \frac{s + 1}{s ^{2} + s + 10}

d er i v a t i v e \frac{sin ( x )}{2 x}

\frac{d y}{d x} = - 4 (y - 5)