(\partial)/(\partial y)(xsin(x^2-y^2))

Lösung

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

- 2 x y cos (x^{2} - y^{2})

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= x cos (x^{2} - y^{2}) (- 2 y)

Vereinfache

= - 2 x y cos (x^{2} - y^{2})

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

h \to π lim (\frac{cos ( 2 )}{3})

x \to - 1 lim (6 x^{2} + 4 x - 2)

x \to 1 lim (5 x - x^{2})

d er i v a t i v e e - 5 x + e^{3} x