derivative y=7x^{1/2}+x^{3/2}

Lösung

ableitung von

y = 7 x^{\frac{1}{2}} + x^{\frac{3}{2}}

\frac{7}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2}

Schritte zur Lösung

\frac{d}{d x} (7 x^{\frac{1}{2}} + x^{\frac{3}{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (7 x^{\frac{1}{2}}) + \frac{d}{d x} (x^{\frac{3}{2}})

\frac{d}{d x} (7 x^{\frac{1}{2}}) = \frac{7}{2 x ^{\frac{1}{2}}}

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

= \frac{7}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2}

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