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Beliebt Rechnen >

implicit 3x^3+9xy^2=5x^3

Lösung

implizite ableitung

3 x^{3} + 9 x y^{2} = 5 x^{3}

Lösung

\frac{d y}{d x} = \frac{2 x ^{2} - 3 y ^{2}}{6 x y}

Schritte zur Lösung

3 x^{3} + 9 x y^{2} = 5 x^{3}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

9 x^{2} + 9 (y^{2} + 2 x y \frac{d y}{d x}) = 15 x^{2}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{2 x ^{2} - 3 y ^{2}}{6 x y}

\frac{d y}{d x} = \frac{2 x ^{2} - 3 y ^{2}}{6 x y}

Beliebte Beispiele

derivative of e^{((x^2)/2})

\frac{d}{d x} (e^{\frac{( x ^{2} )}{2}})

y^{''}-4y^'+4y=t^3y^0

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3} y^{0}

(d^2)/(dx^2)(e^{3x}cos(2x))

\frac{d ^{2}}{d x ^{2}} (e^{3 x} cos (2 x))

derivative of 9sin(xcos(x))

\frac{d}{d x} (9 sin (x) cos (x))

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

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