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Beliebt Rechnen >

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

Lösung

\frac{d}{d x} (e^{(x + l n (x))})

Lösung

e^{x} x + e^{x}

Schritte zur Lösung

\frac{d}{d x} (e^{(x + l n (x))})

Vereinfache

e^{(x + l n (x))} : e^{x} x

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

Wende die Produktregel an:

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

f = e^{x}, g = x

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

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

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

= e^{x} x + 1 \cdot e^{x}

Vereinfache

= e^{x} x + e^{x}

Graph

Beliebte Beispiele

fläche y=sin(x),y=sin(2x),x=0,x= pi/3

a re a y = sin (x), y = sin (2 x), x = 0, x = \frac{π}{3}

derivative of 1-ln(cos(x))

\frac{d}{d x} (1 - ln (cos (x)))

derivative f(x)=(x^2-4)/(x-3)

d er i v a t i v e f (x) = \frac{x ^{2} - 4}{x - 3}

limit as x approaches-infinity of a^x

x \to - \infty lim (a^{x})

integral of y^2ln(y)

\int y^{2} ln (y) d y