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

Lösung

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

y - 2 x

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (4) = 0

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

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

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

= 0 - 2 x + y - 0

Vereinfache

= y - 2 x

t an g e n t x^{2} + y^{2} = 29, (- 5, 2)

\int_{0}^{1} \frac{x ^{2}}{1 + x ^{6}} d x

\int e^{- 2 l n (x)} d x

\frac{\partial}{\partial x} (e^{x z} + x y)

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