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

Lösung

ableitung von

5 t + 6 t^{5}

\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

\frac{d}{d t} (5 t + 6 t^{5})

Wende die Summen-/Differenzregel an:

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

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

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

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

= \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}}}

x \to 2 - lim (x 4 - x^{2})

\frac{d}{d x} (8 x e^{6 x})

\frac{d}{d x} (\frac{3 x ^{2} - 9 x + 1}{7 x + 8})

\int \frac{18 - 18 x}{1 - x} d x

x \to 0 + lim ((5 x)^{2 x})