(\partial)/(\partial x)(e^{4(e^x-1)})

Lösung

\frac{\partial}{\partial x} (e^{4 (e^{x} - 1)})

4 e^{4 (e^{x} - 1) + x}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{4 (e^{x} - 1)})

Wende die Kettenregel an:

e^{4 (e^{x} - 1)} \frac{\partial}{\partial x} (4 (e^{x} - 1))

= e^{4 (e^{x} - 1)} \frac{\partial}{\partial x} (4 (e^{x} - 1))

\frac{\partial}{\partial x} (4 (e^{x} - 1)) = 4 e^{x}

= e^{4 (e^{x} - 1)} \cdot 4 e^{x}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

e^{4 (e^{x} - 1)} e^{x} = e^{4 (e^{x} - 1) + x}

= 4 e^{4 (e^{x} - 1) + x}

x \to 0 lim ((1 - 6 x)^{\frac{6}{x}})

\frac{\partial}{\partial y} (3 x^{4} y^{2} + 3)

y^{3} y^{^{'}} + x^{3} = 0

t an g e n t x^{2} + 2 x

\int (6 x^{2} - 8 x + 2) d x