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Beliebt Rechnen >

derivative f(x)=4sqrt(x^3)

Lösung

ableitung von

f (x) = 4 x^{3}

Lösung

6 x

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Radikal Regel an:

n a^{m} = a^{\frac{m}{n}}

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

Wende die Potenzregel an:

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

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

Vereinfache

4 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : 6 x

= 6 x

Graph

Beliebte Beispiele

derivative of ln(1+xy)

\frac{d}{d x} (ln (1 + x y))

integral of 30(x+7)(x+5)^4

\int 30 (x + 7) (x + 5)^{4} d x

limit as x approaches 8 of (8x)/(x-8)

x \to 8 lim (\frac{8 x}{x - 8})

y^'=(1-2t)y^2,y(0)=-1/6

y^{^{'}} = (1 - 2 t) y^{2}, y (0) = - \frac{1}{6}

integral of x^3sqrt(x^2+24)

\int x^{3} x^{2} + 24 d x