(\partial)/(\partial y)(x^4-x^2y^3)

Lösung

\frac{\partial}{\partial y} (x^{4} - x^{2} y^{3})

- 3 x^{2} y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{4} - x^{2} y^{3})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{4}) - \frac{\partial}{\partial y} (x^{2} y^{3})

\frac{\partial}{\partial y} (x^{4}) = 0

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

= 0 - 3 x^{2} y^{2}

Vereinfache

= - 3 x^{2} y^{2}

\int_{0}^{1} (10 + x x) d x

y^{^{''}} + y = sin (t), y (0) = 0, y^{^{'}} (0) = 0

x y y^{^{'}} = x^{2} e^{\frac{y}{x}} + y^{2}

(x + 3) (\frac{d y}{d x}) + y = ln (x)

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