(\partial)/(\partial y)(xy-5y+x^2+y^2-10x)

Lösung

\frac{\partial}{\partial y} (x y - 5 y + x^{2} + y^{2} - 10 x)

x + 2 y - 5

Schritte zur Lösung

\frac{\partial}{\partial y} (x y - 5 y + x^{2} + y^{2} - 10 x)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x y) - \frac{\partial}{\partial y} (5 y) + \frac{\partial}{\partial y} (x^{2}) + \frac{\partial}{\partial y} (y^{2}) - \frac{\partial}{\partial y} (10 x)

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

\frac{\partial}{\partial y} (5 y) = 5

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

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

\frac{\partial}{\partial y} (10 x) = 0

= x - 5 + 0 + 2 y - 0

Vereinfache

= x + 2 y - 5

\int 1 - 3 x d x

\int_{0}^{1} e^{- x^{2}} d x

x \to + 0 lim (\frac{1}{x})

y^{^{'}} - \frac{7}{x} y = \frac{y ^{5}}{x ^{5}}

l a pl a ce t r an s f or m e^{5 (t - 2)}