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Beliebt Rechnen >

derivative of 2/5 x^{5/2}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

\frac{2}{5} \cdot \frac{5}{2} x^{\frac{5}{2} - 1} : x^{\frac{3}{2}}

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

Graph

Beliebte Beispiele

integral of (x^3-2x^{1/2}+4)^2

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

derivative of 1/(sqrt(y-5x^2))

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

y^{^{'}} - y = 2 t

x^2y^'+2xy=25cos^2(x)

x^{2} y^{^{'}} + 2 x y = 25 cos^{2} (x)

tangent (-8x)/(x^2+1)

t an g e n t \frac{- 8 x}{x ^{2} + 1}