implicit (dy)/(dx),3(x^2+y^2)^2=100xy

Lösung

implizite ableitung

\frac{d y}{d x}, 3 (x^{2} + y^{2})^{2} = 100 x y

\frac{d y}{d x} = \frac{25 y - 3 x ^{3} - 3 x y ^{2}}{3 y ^{3} - 25 x + 3 x ^{2} y}

Schritte zur Lösung

3 (x^{2} + y^{2})^{2} = 100 x y

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

6 (x^{2} + y^{2}) (2 x + 2 y \frac{d y}{d x}) = 100 (y + x \frac{d y}{d x})

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{25 y - 3 x ^{3} - 3 x y ^{2}}{3 y ^{3} - 25 x + 3 x ^{2} y}

\frac{d y}{d x} = \frac{25 y - 3 x ^{3} - 3 x y ^{2}}{3 y ^{3} - 25 x + 3 x ^{2} y}

\frac{d}{d x} (\frac{a ^{2} x}{( x + b ) ^{2}})

\frac{d}{d x} (3 \frac{3 x}{4 π})

x \to - 3 lim (\frac{4 x - 5}{3 x + 9})

x \to 1 lim ([3 x + 1])

\int (1 + 6 x)^{4} (6) d x