derivative x^4e^x

Lösung

ableitung von

x^{4} e^{x}

4 x^{3} e^{x} + e^{x} x^{4}

Schritte zur Lösung

\frac{d}{d x} (x^{4} e^{x})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{4}, g = e^{x}

= \frac{d}{d x} (x^{4}) e^{x} + \frac{d}{d x} (e^{x}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (e^{x}) = e^{x}

= 4 x^{3} e^{x} + e^{x} x^{4}

\int (e^{y} + 1)^{- 2} e^{y} d y

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

\frac{d ^{2}}{d x ^{2}} (sin (b x) - 2 cos (b x))

\int \frac{1}{b x} d x

h \to 0 lim ((1 + h)^{\frac{1}{h}})