erweitern (dx)/(yx)(x^2+y^2=1)

Lösung

erweitern

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

\frac{x d x}{y} + \frac{y d x}{x} = 1

Schritte zur Lösung

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

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

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

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

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

Multipliziere aus

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

\frac{x d x}{y} + \frac{y d x}{x} = 1

e x p an d sin (2 (t - π))

e x p an d \frac{\frac{d}{d x} ( ( 2 x + 7 ) ( x ^{2} + 3 ) )}{( 3 x + 5 )}

\frac{d ^{2}}{d x ^{2}} ((y) (x + 10 x^{2}))

s im pl i f y (\frac{x + 7}{x} + 3 x) 10

e x p an d \frac{6}{( x + 4 ) ( x - 1 )}