derivative y=(x-1)^{3/2}+(e^{x-2})/2

Lösung

ableitung von

y = (x - 1)^{\frac{3}{2}} + \frac{e ^{x - 2}}{2}

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

\frac{3 ( x - 1 ) ^{\frac{1}{2}}}{2} + \frac{1}{2} e^{x - 2} : \frac{3 ( x - 1 ) ^{\frac{1}{2}} + e ^{x - 2}}{2}

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

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