derivative f(t)=-(50)/(t^3)+5/(t^2)

Lösung

ableitung von

f (t) = - \frac{50}{t ^{3}} + \frac{5}{t ^{2}}

\frac{150}{t ^{4}} - \frac{10}{t ^{3}}

Schritte zur Lösung

\frac{d}{d t} (- \frac{50}{t ^{3}} + \frac{5}{t ^{2}})

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d t} (\frac{50}{t ^{3}}) + \frac{d}{d t} (\frac{5}{t ^{2}})

\frac{d}{d t} (\frac{50}{t ^{3}}) = - \frac{150}{t ^{4}}

\frac{d}{d t} (\frac{5}{t ^{2}}) = - \frac{10}{t ^{3}}

= - (- \frac{150}{t ^{4}}) - \frac{10}{t ^{3}}

Vereinfache

= \frac{150}{t ^{4}} - \frac{10}{t ^{3}}

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