derivative of (12/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{12}{x})

- \frac{6}{x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{12}{x})

Entferne die Konstante:

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

= 12 \frac{d}{d x} (\frac{1}{x})

Wende Exponentenregel an:

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

= 12 \frac{d}{d x} (x^{- \frac{1}{2}})

Wende die Potenzregel an:

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

= 12 (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Vereinfache

12 (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{6}{x ^{\frac{3}{2}}}

= - \frac{6}{x ^{\frac{3}{2}}}

\int_{0}^{4} \frac{1}{x ^{2} - 16} d x

x \to 4 lim (\frac{5 - x}{x - 4})

a re a 6 x, 8 x^{2}, (0, 0.75)

\frac{d}{d x} (c e^{5 t} + c e^{5 y (t, x)})

\int_{4.5}^{5} \frac{x}{8} d x