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

Lösung

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

x^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= 0 + x^{2}

Vereinfache

= x^{2}

\frac{d y}{d x} = \frac{( 2 x ( y - 2 ) )}{x ^{2} + 1}, y (0) = 4

t \to 0 lim (e^{- t})

d er i v a t i v e y = \frac{1}{2} (e^{x} + e^{- x})

\int 2 x (x^{2} - 7)^{99} d x

\frac{\partial}{\partial y} (e^{x y z^{8}} y z^{8})