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Beliebt Rechnen >

derivative y=1+x-4x^{1/2}

Lösung

ableitung von

y = 1 + x - 4 x^{\frac{1}{2}}

Lösung

- \frac{2}{x ^{\frac{1}{2}}} + 1

Schritte zur Lösung

\frac{d}{d x} (1 + x - 4 x^{\frac{1}{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (1) + \frac{d x}{d x} - \frac{d}{d x} (4 x^{\frac{1}{2}})

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

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

\frac{d}{d x} (4 x^{\frac{1}{2}}) = \frac{2}{x ^{\frac{1}{2}}}

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

Vereinfache

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

Graph

Beliebte Beispiele

derivative arctan((1+x)/(1-x))

d er i v a t i v e arctan (\frac{1 + x}{1 - x})

2+(dy)/(dx)=sqrt(2x+y)

2 + \frac{d y}{d x} = 2 x + y

derivative of (inx/x)

\frac{d}{d x} (\frac{in x}{x})

limit as x approaches 8 of e^{3/((x-8))}

x \to 8 lim (e^{\frac{3}{( x - 8 )}})

integral of 2/(x-2)

\int \frac{2}{x - 2} d x