(\partial)/(\partial x)(9/x+3/y+xy)

Lösung

\frac{\partial}{\partial x} (\frac{9}{x} + \frac{3}{y} + x y)

y - \frac{9}{x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{9}{x} + \frac{3}{y} + x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (\frac{9}{x}) + \frac{\partial}{\partial x} (\frac{3}{y}) + \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

\frac{\partial}{\partial x} (\frac{3}{y}) = 0

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

= - \frac{9}{x ^{2}} + 0 + y

Vereinfache

= y - \frac{9}{x ^{2}}

\frac{d}{d x} (x^{a r c t a n (x)})

\frac{d y}{d x} + 6 (tan (6 x)) y = 9 cos (6 x)

\frac{d}{d x} (8 x^{2} - x^{3})

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

x \to - 2 lim (\frac{∣ x - 2 ∣}{x - 2})