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Beliebt Rechnen >

implicit (dy)/(dx),x^3-3xy^2+y^3=1

Lösung

implizite ableitung

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

Lösung

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

Schritte zur Lösung

x^{3} - 3 x y^{2} + y^{3} = 1

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

3 x^{2} - 3 (y^{2} + 2 x y \frac{d y}{d x}) + 3 y^{2} \frac{d y}{d x} = 0

Isoliere

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

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

Beliebte Beispiele

y^'=3x+y,y(0)=5

y^{^{'}} = 3 x + y, y (0) = 5

tangent y=2sqrt(x),(1,2)

t an g e n t y = 2 x, (1, 2)

integral of 1/((x)ln(x))

\int \frac{1}{( x ) ln ( x )} d x

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

\frac{d}{d x} (\frac{( x ^{2} )}{x ^{2} + 4})

sum from n=0 to infinity of-6(1/4)^{2n}

n = 0 \sum \infty - 6 (\frac{1}{4})^{2 n}