(\partial)/(\partial x)(2y-1/x+cos(3x))

Lösung

\frac{\partial}{\partial x} (2 y - \frac{1}{x} + cos (3 x))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (2 y - \frac{1}{x} + cos (3 x))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2 y) - \frac{\partial}{\partial x} (\frac{1}{x}) + \frac{\partial}{\partial x} (cos (3 x))

\frac{\partial}{\partial x} (2 y) = 0

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

\frac{\partial}{\partial x} (cos (3 x)) = - sin (3 x) \cdot 3

= 0 - (- \frac{1}{x ^{2}}) - sin (3 x) \cdot 3

Vereinfache

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

\int x^{3} x^{4} + 9 d x

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

x \to 1 lim (\frac{x + 4}{x + 2})

\frac{d}{d x} (4 + 3 x)

x \to \infty lim (1 - 2 x)