derivative of 1/(4x^{3/4})

Lösung

\frac{d}{d x} (\frac{1}{4 x ^{\frac{3}{4}}})

- \frac{3}{16 x ^{\frac{7}{4}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{4 x ^{\frac{3}{4}}})

Entferne die Konstante:

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

= \frac{1}{4} \frac{d}{d x} (\frac{1}{x ^{\frac{3}{4}}})

Wende Exponentenregel an:

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

= \frac{1}{4} \frac{d}{d x} (x^{- \frac{3}{4}})

Wende die Potenzregel an:

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

= \frac{1}{4} (- \frac{3}{4} x^{- \frac{3}{4} - 1})

Vereinfache

\frac{1}{4} (- \frac{3}{4} x^{- \frac{3}{4} - 1}) : - \frac{3}{16 x ^{\frac{7}{4}}}

= - \frac{3}{16 x ^{\frac{7}{4}}}

\frac{\partial}{\partial x} (1.85 + 2.05 x + 0.656 y)

x \to 0 lim (sin (1 x))

n = 1 \sum \infty e^{- n}

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

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