(\partial)/(\partial x)(1/(x^2)+y)

Lösung

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

- \frac{2}{x ^{3}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

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

= - \frac{2}{x ^{3}} + 0

Vereinfache

= - \frac{2}{x ^{3}}

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

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0, y^{^{'}} (0) = 4

\frac{\partial}{\partial x} (sin (x) cosh (y))

\frac{d y}{d x} = 1 + x + y + x \cdot y

x \to \infty lim ((1 + \frac{5}{x})^{\frac{x}{7}})