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Beliebt Rechnen >

implicit (dy)/(dx),x^2y=1

Lösung

implizite ableitung

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

Lösung

\frac{d y}{d x} = - \frac{2 y}{x}

Schritte zur Lösung

x^{2} y = 1

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

2 x y + \frac{d y}{d x} x^{2} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{2 y}{x}

\frac{d y}{d x} = - \frac{2 y}{x}

Beliebte Beispiele

integral of (2x)/(λ^2)

\int \frac{2 x}{λ ^{2}} d x

limit as x approaches 0 of (e^{4x}-1)/(2x^2+2x)

x \to 0 lim (\frac{e ^{4 x} - 1}{2 x ^{2} + 2 x})

integral of sin(x)sin(n)x

\int sin (x) sin (n) x d x

sum from n=1 to infinity of 4/(n(n+6))

n = 1 \sum \infty \frac{4}{n ( n + 6 )}

integral of sin^4(x)cos^3(x)

\int sin^{4} (x) cos^{3} (x) d x