(\partial)/(\partial x)(5-x^2+xy-3y^2)

Lösung

\frac{\partial}{\partial x} (5 - x^{2} + x y - 3 y^{2})

y - 2 x

Schritte zur Lösung

\frac{\partial}{\partial x} (5 - x^{2} + x y - 3 y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (5) - \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (x y) - \frac{\partial}{\partial x} (3 y^{2})

\frac{\partial}{\partial x} (5) = 0

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 0 - 2 x + y - 0

Vereinfache

= y - 2 x

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

x^{2} y^{^{''}} - 2 x y^{^{'}} + 2 y = x^{4} e^{x}

\int \frac{1}{2} y^{2} d y

in v erse l a pl a ce \frac{s + 2}{s ^{2} + 4 s + 5}

y^{^{''}} + 25 y = t sin (4 t)