derivative of (sqrt(x)/5)

Lösung

\frac{d}{d x} (\frac{x}{5})

\frac{1}{10 x}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{5})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Radikal Regel an:

a = a^{\frac{1}{2}}

= \frac{1}{5} \frac{d}{d x} (x^{\frac{1}{2}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{5} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Vereinfache

\frac{1}{5} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{1}{10 x}

= \frac{1}{10 x}

x \to 0 lim (x (13 + \frac{5}{x}))

\int \frac{sec ^{2} ( x )}{6 + 2 tan ^{2} ( x )} d x

d er i v a t i v e f (x) = \frac{1}{2} b (\frac{1}{x} - \frac{1}{x ^{0}})^{2}

t an g e n t f (x) = x^{3} - 5 x^{2} + 7, at x = 1

\int \frac{x + 5}{x ^{2} + 2 x - 15} d x