derivative of xe^xln(x)

Lösung

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

e^{x} ln (x) + e^{x} x ln (x) + e^{x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = e^{x} ln (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x} ln (x) + (e^{x} ln (x) + \frac{e ^{x}}{x}) x

Vereinfache

1 \cdot e^{x} ln (x) + (e^{x} ln (x) + \frac{e ^{x}}{x}) x : e^{x} ln (x) + e^{x} x ln (x) + e^{x}

= e^{x} ln (x) + e^{x} x ln (x) + e^{x}

d er i v a t i v e f (x) = 1 - y^{2}

\frac{d y}{d x} - tan (x) y = e^{11 x}

n = 1 \sum \infty \frac{3}{n ^{6}}

\frac{d}{d x} (\frac{( x - 3 )}{x - 3})

x \to 0 lim (\frac{x ^{2} - 1}{x ^{2}})