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Beliebt Rechnen >

derivative of x+log_{e}(x)

Lösung

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

Lösung

1 + \frac{1}{x}

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 Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 1 + \frac{1}{x}

Graph

Beliebte Beispiele

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

(dx)/(dt)-4x=cos(5t)

\frac{d x}{d t} - 4 x = cos (5 t)

tangent f(x)=-3x^3-2x^2-x+3,(-,5)

t an g e n t f (x) = - 3 x^{3} - 2 x^{2} - x + 3, (-, 5)

sum from n=1 to infinity of 1/(n^7)

n = 1 \sum \infty \frac{1}{n ^{7}}

integral of sin(12x)cos(9x)

\int sin (12 x) cos (9 x) d x