(\partial)/(\partial y)(x^2+sin(xy))

Lösung

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

x cos (x y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= 0 + cos (x y) x

Vereinfache

= x cos (x y)

4 y^{^{''}} - y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 0

x \to 3 lim (\frac{3 - x}{∣ 3 - x ∣})

x \to - \infty lim (0^{x})

x \to 0 + lim (ln (5) sin (x))

\int_{4}^{16} \frac{1}{6 - x} d x