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Beliebt Rechnen >

derivative of sqrt(3x^2+y^2-1)

Lösung

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

Lösung

\frac{3 x + y \frac{d y}{d x}}{3 x ^{2} + y ^{2} - 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (3 x^{2} + y^{2} - 1) = 6 x + 2 y \frac{d y}{d x}

= \frac{1}{2 3 x ^{2} + y ^{2} - 1} (6 x + 2 y \frac{d y}{d x})

Vereinfache

\frac{1}{2 3 x ^{2} + y ^{2} - 1} (6 x + 2 y \frac{d y}{d x}) : \frac{3 x + y \frac{d y}{d x}}{3 x ^{2} + y ^{2} - 1}

= \frac{3 x + y \frac{d y}{d x}}{3 x ^{2} + y ^{2} - 1}

Beliebte Beispiele

integral from 0 to 1 of (x-x^4)

\int_{0}^{1} (x - x^{4}) d x

fläche y=3x,y=7x^2

a re a y = 3 x, y = 7 x^{2}

derivative of f(x(4x^2-2))

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

derivative of (2x/(5-tan(x)))

\frac{d}{d x} (\frac{2 x}{5 - tan ( x )})

derivative of (2x+5/(3x-1))

\frac{d}{d x} (\frac{2 x + 5}{3 x - 1})