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Beliebt Rechnen >

derivative of 1200sqrt(x^2-0.2x)

Lösung

\frac{d}{d x} (1200 x^{2} - 0.2 x)

Lösung

\frac{600 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

Schritte zur Lösung

\frac{d}{d x} (1200 x^{2} - 0.2 x)

Entferne die Konstante:

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

= 1200 \frac{d}{d x} (x^{2} - 0.2 x)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} - 0.2 x} \frac{d}{d x} (x^{2} - 0.2 x)

= \frac{1}{2 x ^{2} - 0.2 x} \frac{d}{d x} (x^{2} - 0.2 x)

\frac{d}{d x} (x^{2} - 0.2 x) = 2 x - 0.2

= 1200 \cdot \frac{1}{2 x ^{2} - 0.2 x} (2 x - 0.2)

Vereinfache

1200 \cdot \frac{1}{2 x ^{2} - 0.2 x} (2 x - 0.2) : \frac{600 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

= \frac{600 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

Graph

Beliebte Beispiele

derivative of x^3-12x-5

\frac{d}{d x} (x^{3} - 12 x - 5)

derivative of 2-4x

\frac{d}{d x} (2 - 4 x)

integral of 1/(sqrt(4x^2+2))

\int \frac{1}{4 x ^{2} + 2} d x

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\int_{0}^{π} t^{2} e^{- s t} d t

fläche y=e^x,y=e^{-x},x=1

a re a y = e^{x}, y = e^{- x}, x = 1