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Beliebt Rechnen >

derivative f(x)=x+sqrt(x)+1

Lösung

ableitung von

f (x) = x + x + 1

Lösung

\frac{1}{2 x} + 1

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (1) = 0

= 1 + \frac{1}{2 x} + 0

Vereinfache

= \frac{1}{2 x} + 1

Graph

Beliebte Beispiele

derivative of-λx

\frac{d}{d x} (- λ x)

limit as x approaches 0 of (x+sin(x))/x

x \to 0 lim (\frac{x + sin ( x )}{x})

derivative e^{5/x}

d er i v a t i v e e^{\frac{5}{x}}

(\partial)/(\partial x)((y-x)^2)

\frac{\partial}{\partial x} ((y - x)^{2})

fläche 2/x ,8x, 1/8 x

a re a \frac{2}{x}, 8 x, \frac{1}{8} x