d/(dt)((t^3)/6+(t^2)/4+1/2 t)

Lösung

\frac{d}{d t} (\frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{1}{2} t)

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

Schritte zur Lösung

\frac{d}{d t} (\frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{1}{2} t)

Vereinfache

\frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{1}{2} t : \frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{t}{2}

= \frac{d}{d t} (\frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{t}{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (\frac{t ^{3}}{6}) + \frac{d}{d t} (\frac{t ^{2}}{4}) + \frac{d}{d t} (\frac{t}{2})

\frac{d}{d t} (\frac{t ^{3}}{6}) = \frac{t ^{2}}{2}

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

\frac{d}{d t} (\frac{t}{2}) = \frac{1}{2}

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

Wende Regel an

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 7} d x

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l a pl a ce t r an s f or m e^{t} sin (t)

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