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

Lösung

ableitung von

5 t + 6 t^{5}

\frac{1 + 75 t ^{\frac{23}{10}}}{5 t ^{\frac{4}{5}}}

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}) = 15 t^{\frac{3}{2}}

= \frac{1}{5 t ^{\frac{4}{5}}} + 15 t^{\frac{3}{2}}

Vereinfache

\frac{1}{5 t ^{\frac{4}{5}}} + 15 t^{\frac{3}{2}} : \frac{1 + 75 t ^{\frac{23}{10}}}{5 t ^{\frac{4}{5}}}

= \frac{1 + 75 t ^{\frac{23}{10}}}{5 t ^{\frac{4}{5}}}

\frac{d}{d x} (x (1 - x))

y^{^{'}} + 2 y = 0

x \to \infty lim (7 + \frac{6}{x})

im pl i c i t \frac{d y}{d x}, y = \frac{1}{x}

\int \frac{1}{( x - 1 )} d x