(\partial)/(\partial y)(0.5x^2+y^2-3x+2y-5)

Lösung

\frac{\partial}{\partial y} (0.5 x^{2} + y^{2} - 3 x + 2 y - 5)

2 y + 2

Schritte zur Lösung

\frac{\partial}{\partial y} (0.5 x^{2} + y^{2} - 3 x + 2 y - 5)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (0.5 x^{2}) + \frac{\partial}{\partial y} (y^{2}) - \frac{\partial}{\partial y} (3 x) + \frac{\partial}{\partial y} (2 y) - \frac{\partial}{\partial y} (5)

\frac{\partial}{\partial y} (0.5 x^{2}) = 0

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

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

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

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

= 0 + 2 y - 0 + 2 - 0

Vereinfache

= 2 y + 2

\frac{d}{d x} (ln (a x + b))

x \cdot \frac{d y}{d x} + 2 y = 3 x

\int \frac{1}{1 + cosh ( x )} d x

\frac{\partial}{\partial y} (5 x^{3} y^{6})

\frac{y ^{^{'}} + 0.3334 y}{( 20.004 x + 6000 )} = 20