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Beliebt Rechnen >

derivative of 1/3*(x-5^3)

Lösung

\frac{d}{d x} (\frac{1}{3} \cdot (x - 5)^{3})

Lösung

(x - 5)^{2}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} (x - 5)^{3})

Entferne die Konstante:

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

= \frac{1}{3} \frac{d}{d x} ((x - 5)^{3})

Wende die Kettenregel an:

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

= 3 (x - 5)^{2} \frac{d}{d x} (x - 5)

\frac{d}{d x} (x - 5) = 1

= \frac{1}{3} \cdot 3 (x - 5)^{2} \cdot 1

Vereinfache

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

= (x - 5)^{2}

Graph

Beliebte Beispiele

derivative of 2sin(x+5cos(3pix))

\frac{d}{d x} (2 sin (x) + 5 cos (3 π x))

derivative of (x^4+5x^2)

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integral of (3/x+x/3)

\int (\frac{3}{x} + \frac{x}{3}) d x

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\int sin (x) sin (4 x) d x

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\frac{d}{d x} (e^{x + 7})