erweitern (dx)/d (y^2+6yx+x^2=8)

Lösung

erweitern

\frac{d x}{d} (y^{2} + 6 y x + x^{2} = 8)

\frac{y ^{2} d x}{d} + \frac{6 x y d x}{d} + \frac{x ^{2} d x}{d} = 8

Schritte zur Lösung

\frac{d x}{d} (y^{2} + 6 y x + x^{2} = 8)

= \frac{d x}{d} (y^{2} + 6 x y + 8 = x^{2})

Setze Klammern

\frac{d x}{d} y^{2} + \frac{d x}{d} \cdot 6 y x + \frac{d x}{d} x^{2} = 8

\frac{d x}{d} y^{2} + 6 \cdot \frac{d x}{d} x y + \frac{d x}{d} x^{2} = 8

Multipliziere aus

\frac{d x}{d} y^{2} + 6 \cdot \frac{d x}{d} x y + \frac{d x}{d} x^{2} : \frac{y ^{2} d x}{d} + \frac{6 x y d x}{d} + \frac{x ^{2} d x}{d}

\frac{y ^{2} d x}{d} + \frac{6 x y d x}{d} + \frac{x ^{2} d x}{d} = 8

e x p an d \frac{( ( x + 1 ) ( x - 1 ) )}{( x )}

e x p an d (3 x + 1) \frac{( x + 2 )}{( x - 1 = 0 )}

e x p an d \frac{4 + x}{3 1 - 2 x}

e x p an d (x + y) e^{- x^{2} - y^{2}}

e x p an d (4 z + x^{2} z) d z + (1 + z^{2}) x d x - (y z^{2} + y) (4 + x^{2}) d y