(\partial)/(\partial x)(xy^2+ye^{x^2}+5)

Lösung

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

y^{2} + 2 e^{x^{2}} x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= y^{2} + y e^{x^{2}} \cdot 2 x + 0

Vereinfache

= y^{2} + 2 e^{x^{2}} x y

\frac{d y}{d x} + 2 x y = 2 x^{3}, y (0) = 2

\frac{d y}{d x} + y = x y^{2}

d er i v a t i v e y = ln (t^{2}) - arctan (\frac{t}{3})

d er i v a t i v e \frac{t + 1710}{50 ( t + 2 )}

in v erse l a pl a ce - \frac{2}{s ^{3} ( s - 3 )}