(\partial)/(\partial y)(cos(xy)x)

Lösung

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

- x^{2} sin (x y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= x (- sin (x y) x)

Vereinfache

x (- sin (x y) x) : - x^{2} sin (x y)

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

\frac{d}{d x} ((x^{2} - \frac{2}{3})^{\frac{3}{2}})

d er i v a t i v e \frac{7}{ln ( x )}

\frac{d}{d y} (\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}})

\int (4 x^{3} + 3 x^{2} + 2 x + 1) d x

d er i v a t i v e \frac{1}{t}