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Beliebt Rechnen >

implicit (dy)/(dx),-x+y-x^3=y^3+4x^2

Lösung

implizite ableitung

\frac{d y}{d x}, - x + y - x^{3} = y^{3} + 4 x^{2}

Lösung

\frac{d y}{d x} = \frac{8 x + 3 x ^{2} + 1}{1 - 3 y ^{2}}

Schritte zur Lösung

- x + y - x^{3} = y^{3} + 4 x^{2}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

- 1 + \frac{d y}{d x} - 3 x^{2} = 3 y^{2} \frac{d y}{d x} + 8 x

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{8 x + 3 x ^{2} + 1}{1 - 3 y ^{2}}

\frac{d y}{d x} = \frac{8 x + 3 x ^{2} + 1}{1 - 3 y ^{2}}

Beliebte Beispiele

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

\int \frac{( x + 1 ) ^{2}}{x ^{2}} d x

integral of 1/(n(n+1))

\int \frac{1}{n ( n + 1 )}

y^{''}-3y^'-18y=0

y^{^{''}} - 3 y^{^{'}} - 18 y = 0

fläche x^3-15x^2+50x,-x^3+15x^2-50x

a re a x^{3} - 15 x^{2} + 50 x, - x^{3} + 15 x^{2} - 50 x

sum from n=0 to infinity of 1/(2n+3)

n = 0 \sum \infty \frac{1}{2 n + 3}