(\partial)/(\partial y)(ycos(xy)+e^x)

Lösung

\frac{\partial}{\partial y} (y cos (x y) + e^{x})

cos (y x) - y x sin (y x)

Schritte zur Lösung

\frac{\partial}{\partial y} (y cos (x y) + e^{x})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (y cos (x y)) + \frac{\partial}{\partial y} (e^{x})

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

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

= cos (x y) - x y sin (x y) + 0

Vereinfache

= cos (y x) - y x sin (y x)

d er i v a t i v e 3 3 x^{4} + 4 x^{3}

\int cos^{2} (t) - sin^{2} (t) d t

\frac{\partial}{\partial x} (sin (x^{1} y^{3}))

e x p an d (- 2 cos (2 x) - sin (3 x))^{2}

x \to \frac{1}{2} lim (arcsin (x))