(\partial)/(\partial x)(4+x+x^2Y(x))

Lösung

\frac{\partial}{\partial x} (4 + x + x^{2} Y (x))

x^{2} \frac{\partial}{\partial x} (Y (x)) + 2 x Y (x) + 1

Schritte zur Lösung

\frac{\partial}{\partial x} (4 + x + x^{2} Y (x))

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4) + \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (x^{2} Y (x))

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

\frac{\partial}{\partial x} (x) = 1

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

= 0 + 1 + 2 x Y (x) + \frac{\partial}{\partial x} (Y (x)) x^{2}

Vereinfache

= x^{2} \frac{\partial}{\partial x} (Y (x)) + 2 x Y (x) + 1

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

\int 2 x + 9 x^{- 2} d x

y^{^{'}} - \frac{1}{x} y = x^{2} y^{4}

t an g e n t f (x) = 3 x^{2} - 3 x - 5

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