derivative \sqrt[5]{t}+\sqrt[6]{t^5}

Lösung

ableitung von

\frac{6 ( t ^{5} ) ^{\frac{5}{6}} + 25 t ^{\frac{24}{5}}}{30 t ^{\frac{4}{5}} ( t ^{5} ) ^{\frac{5}{6}}}

Schritte zur Lösung

Wende die Summen-/Differenzregel an:

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

= \frac{1}{5 t ^{\frac{4}{5}}} + \frac{5 t ^{4}}{6 ( t ^{5} ) ^{\frac{5}{6}}}

Vereinfache

\frac{1}{5 t ^{\frac{4}{5}}} + \frac{5 t ^{4}}{6 ( t ^{5} ) ^{\frac{5}{6}}} : \frac{6 ( t ^{5} ) ^{\frac{5}{6}} + 25 t ^{\frac{24}{5}}}{30 t ^{\frac{4}{5}} ( t ^{5} ) ^{\frac{5}{6}}}

= \frac{6 ( t ^{5} ) ^{\frac{5}{6}} + 25 t ^{\frac{24}{5}}}{30 t ^{\frac{4}{5}} ( t ^{5} ) ^{\frac{5}{6}}}