d/(d{x)}(({z}(x,y))({x}^2+{y}^2+{x}{y}))

Lösung

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

z (x, y) (2 x + 0 + y)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (y^{2}) = 0

\frac{d}{d x} (x y) = y

= z (x, y) (2 x + 0 + y)

e x p an d y (6 - 3 y - x)^{2}

s im pl i f y (x^{2} - \frac{2 - 3}{6})^{2}

e x p an d x (x^{5} e^{13 x} + 3)

e x p an d tan (x) (tan (x) - 1)

e x p an d (1 - sin (x)) (1 + sin (x))