derivative \sqrt[5]{x}+4sqrt(x^5)

Lösung

ableitung von

5 x + 4 x^{5}

\frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

Schritte zur Lösung

\frac{d}{d x} (5 x + 4 x^{5})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x) + \frac{d}{d x} (4 x^{5})

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

\frac{d}{d x} (4 x^{5}) = 10 x^{\frac{3}{2}}

= \frac{1}{5 x ^{\frac{4}{5}}} + 10 x^{\frac{3}{2}}

Vereinfache

\frac{1}{5 x ^{\frac{4}{5}}} + 10 x^{\frac{3}{2}} : \frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

= \frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

s l o p e (- 3, \frac{2}{5}), (4, \frac{3}{10})

h \to 0 lim (\frac{\frac{1}{1 + h} - 1}{h})

\int \frac{5}{6} x^{\frac{6}{5}} d x

a re a f (x) = 12 x + x^{2} - x^{3}, g (x) = 0

d er i v a t i v e \frac{s - 7}{s + 3}