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

Lösung

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

2 x^{5} v

Schritte zur Lösung

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

Behandle

x, y, u

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial v} (x^{5} v^{2}) = 2 x^{5} v

\frac{\partial}{\partial v} (2 y^{3} u) = 0

\frac{\partial}{\partial v} (3) = 0

= 2 x^{5} v + 0 - 0

Vereinfache

= 2 x^{5} v

\int 2^{\frac{x}{2}} d x

x \cdot \frac{d y}{d x} = 2 x e^{x} - y + 6 x^{2}

\frac{d}{d y} (- x y sin (x) + 2 y cos (x))

y^{^{''}} + y = tan^{2} (x)

x^{2} y^{^{''}} - 2 x y^{^{'}} + 2 y = x^{2}