derivative of x^3+x^{1/2}+2

Lösung

\frac{d}{d x} (x^{3} + x^{\frac{1}{2}} + 2)

\frac{1 + 6 x ^{\frac{5}{2}}}{2 x ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} (x^{3} + x^{\frac{1}{2}} + 2)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (x^{\frac{1}{2}}) + \frac{d}{d x} (2)

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

\frac{d}{d x} (2) = 0

= 3 x^{2} + \frac{1}{2 x ^{\frac{1}{2}}} + 0

Vereinfache

3 x^{2} + \frac{1}{2 x ^{\frac{1}{2}}} + 0 : \frac{1 + 6 x ^{\frac{5}{2}}}{2 x ^{\frac{1}{2}}}

= \frac{1 + 6 x ^{\frac{5}{2}}}{2 x ^{\frac{1}{2}}}

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