derivative 2t+4/3 t^{3/2}+(t^2)/2

Lösung

ableitung von

2 t + \frac{4}{3} t^{\frac{3}{2}} + \frac{t ^{2}}{2}

2 + 2 t^{\frac{1}{2}} + t

Schritte zur Lösung

\frac{d}{d t} (2 t + \frac{4}{3} t^{\frac{3}{2}} + \frac{t ^{2}}{2})

Vereinfache

2 t + \frac{4}{3} t^{\frac{3}{2}} + \frac{t ^{2}}{2} : 2 t + \frac{4 t ^{\frac{3}{2}}}{3} + \frac{t ^{2}}{2}

= \frac{d}{d t} (2 t + \frac{4 t ^{\frac{3}{2}}}{3} + \frac{t ^{2}}{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (2 t) + \frac{d}{d t} (\frac{4 t ^{\frac{3}{2}}}{3}) + \frac{d}{d t} (\frac{t ^{2}}{2})

\frac{d}{d t} (2 t) = 2

\frac{d}{d t} (\frac{4 t ^{\frac{3}{2}}}{3}) = 2 t^{\frac{1}{2}}

\frac{d}{d t} (\frac{t ^{2}}{2}) = t

= 2 + 2 t^{\frac{1}{2}} + t

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