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Beliebt Rechnen >

implicit (dy)/(dx),(x-y)^2=2ax

Lösung

implizite ableitung

\frac{d y}{d x}, (x - y)^{2} = 2 a x

Lösung

\frac{d y}{d x} = - \frac{a - x + y}{x - y}

Schritte zur Lösung

(x - y)^{2} = 2 a x

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

2 (x - y) (1 - \frac{d y}{d x}) = 2 a

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{a - x + y}{x - y}

\frac{d y}{d x} = - \frac{a - x + y}{x - y}

Beliebte Beispiele

derivative of (x^3/(x^2+2))

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

derivative of 2x^3-6x^2

\frac{d}{d x} (2 x^{3} - 6 x^{2})

y^'=y(1-0.0002y)

y^{^{'}} = y (1 - 0.0002 y)

inverselaplace 1/((s+2)(s^2-2s+5))

in v erse l a pl a ce \frac{1}{( s + 2 ) ( s ^{2} - 2 s + 5 )}

integral from-3 to-1 of x^2e^{x^3+27}

\int_{- 3}^{- 1} x^{2} e^{x^{3} + 27} d x