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Beliebt Rechnen >

derivative of ln(xe^x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

\frac{1}{x} e^{x} = \frac{e ^{x}}{x}

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

Graph

Beliebte Beispiele

derivative of (5x-4^2)

\frac{d}{d x} ((5 x - 4)^{2})

derivative f(x)=ln(1/x)

d er i v a t i v e f (x) = ln (\frac{1}{x})

\frac{d y}{d t} = y - 2 t

integral of x/(sqrt(x+8))

\int \frac{x}{x + 8} d x

limit as x approaches 2 of 1/(2-5x)

x \to 2 lim (\frac{1}{2 - 5 x})