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Beliebt Rechnen >

derivative 1/(4x^{3/2)}

Lösung

ableitung von

\frac{1}{4 x ^{\frac{3}{2}}}

Lösung

- \frac{3}{8 x ^{\frac{5}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{4 x ^{\frac{3}{2}}})

Entferne die Konstante:

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

= \frac{1}{4} \frac{d}{d x} (\frac{1}{x ^{\frac{3}{2}}})

Wende Exponentenregel an:

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

= \frac{1}{4} \frac{d}{d x} (x^{- \frac{3}{2}})

Wende die Potenzregel an:

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

= \frac{1}{4} (- \frac{3}{2} x^{- \frac{3}{2} - 1})

Vereinfache

\frac{1}{4} (- \frac{3}{2} x^{- \frac{3}{2} - 1}) : - \frac{3}{8 x ^{\frac{5}{2}}}

= - \frac{3}{8 x ^{\frac{5}{2}}}

Graph

Beliebte Beispiele

derivative of (x+3^4)

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

integral from 0 to sqrt(2 of)sqrt(4-x^2)

\int_{0}^{2} 4 - x^{2} d x

(dy)/(dx)=x-y+1

\frac{d y}{d x} = x - y + 1

(\partial)/(\partial x)((2y)/(x+z))

\frac{\partial}{\partial x} (\frac{2 y}{x + z})

integral of (1-x)^5

\int (1 - x)^{5} d x