(\partial)/(\partial x)(x^2-4xy+4y^2+2)

Lösung

\frac{\partial}{\partial x} (x^{2} - 4 x y + 4 y^{2} + 2)

2 x - 4 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} - 4 x y + 4 y^{2} + 2)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (4 y^{2}) + \frac{\partial}{\partial x} (2)

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

\frac{\partial}{\partial x} (4 x y) = 4 y

\frac{\partial}{\partial x} (4 y^{2}) = 0

\frac{\partial}{\partial x} (2) = 0

= 2 x - 4 y + 0 + 0

Vereinfache

= 2 x - 4 y

a re a x, 1, \frac{x ^{2}}{4}

t an g e n t y = 600 - \frac{x ^{2}}{121}

x^{^{'}} = x - x^{2}

\frac{d}{d x} (e^{2 x} + e^{- 2 x})

\int e^{i wt + ib t} d t