(\partial)/(\partial x)(x+y+xy+x/y+y/x)

Lösung

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

y + \frac{1}{y} - \frac{y}{x ^{2}} + 1

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

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

= 1 + 0 + y + \frac{1}{y} - \frac{y}{x ^{2}}

Vereinfache

= y + \frac{1}{y} - \frac{y}{x ^{2}} + 1

y^{^{''}} + y = k

\int_{4}^{5} x^{2} x - 4 d x

\frac{\partial}{\partial t} (\frac{8.31 t}{V ( t )})

x \to 2 lim (\frac{2 x - 6}{x - 1})

x \to 9 - lim (\frac{5 x}{x - 9})