d/(d{x)}(({f}(x,y))(sqrt({x)^2+{y}^2}-1))

Lösung

\frac{d}{d x} ((f (x, y)) (x^{2} + y^{2} - 1))

f (x, y) (\frac{x}{x ^{2} + y ^{2}} - 0)

Schritte zur Lösung

\frac{d}{d x} ((f (x, y)) (x^{2} + y^{2} - 1))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

= f (x, y) (\frac{x}{x ^{2} + y ^{2}} - 0)

e x p an d \frac{( x y - y )}{( x - 1 ) ^{2} + y ^{2}}

e x p an d (2 - x) e^{x} - 1

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

e x p an d 3^{(x - 1)}

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