derivative of sqrt(x)+\sqrt[5]{x}+1/7

Lösung

\frac{d}{d x} (x + 5 x + \frac{1}{7})

\frac{1}{2 x} + \frac{1}{5 x ^{\frac{4}{5}}}

Schritte zur Lösung

\frac{d}{d x} (x + 5 x + \frac{1}{7})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x) + \frac{d}{d x} (5 x) + \frac{d}{d x} (\frac{1}{7})

\frac{d}{d x} (x) = \frac{1}{2 x}

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

\frac{d}{d x} (\frac{1}{7}) = 0

= \frac{1}{2 x} + \frac{1}{5 x ^{\frac{4}{5}}} + 0

Vereinfache

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

x \to \infty lim (e)

\int_{0}^{1} (x + 6) (x - 7) d x

\int (2520 x) 3 5 + 3 x d x

\frac{d ^{2}}{d x ^{2}} (\frac{1 - 4 x}{1 + 4 x})

\frac{d y}{d x} = \frac{e ^{x}}{y + 2}