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

Lösung

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

x + 2

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

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

= 0 + x + 0 + 2 + 0

Vereinfache

= x + 2

\frac{d}{d x} (\frac{1}{x ^{2} + 16})

\int_{0}^{4} 4 x + 9 d x

\int_{- 9}^{9} 81 - x^{2} d x

l a pl a ce t r an s f or m 4 t^{2} - 3 cos (2 t) + 5 e^{- t}

a re a x - 1, x - 1