(\partial)/(\partial y)(sin(xy)+xsin(y))

Lösung

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

cos (x y) x + x cos (y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= cos (x y) x + x cos (y)

n = 0 \sum \infty (\frac{5}{5})^{n}

x y^{^{'}} + 5 y = x^{3} - x

\frac{\partial}{\partial s} (s \cdot cos (t))

f (x) = 6 cos (2 x)

d er i v a t i v e f (x) = \frac{x ^{3} - 8}{x ^{2} + 3}