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Beliebt Rechnen >

derivative y=xlog_{e}(x)

Lösung

ableitung von

y = x lo g_{e} (x)

Lösung

ln (x) + 1

Schritte zur Lösung

\frac{d}{d x} (x lo g_{e} (x))

Vereinfache

x lo g_{e} (x) : x ln (x)

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

Wende die Produktregel an:

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

f = x, g = ln (x)

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

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

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

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

Vereinfache

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

= ln (x) + 1

Graph

Beliebte Beispiele

limit as x approaches 4 of-2x^2+4x-4

x \to 4 lim (- 2 x^{2} + 4 x - 4)

3(dy)/(dx)+8/(xy^2)=0

3 \frac{d y}{d x} + \frac{8}{x y ^{2}} = 0

derivative of 2/(x+5)

\frac{d}{d x} (\frac{2}{x + 5})

derivative of 1/(x+7)

\frac{d}{d x} (\frac{1}{x + 7})

integral of t*cos(nt)

\int t \cdot cos (n t) d t