(\partial)/(\partial y)(y*cos(y-2x))

Lösung

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

cos (y - 2 x) - y sin (y - 2 x)

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = cos (y - 2 x)

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

\frac{\partial}{\partial y} (y) = 1

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

= 1 \cdot cos (y - 2 x) + (- sin (y - 2 x)) y

Vereinfache

= cos (y - 2 x) - y sin (y - 2 x)

d er i v a t i v e f (x) = x^{2} - x + 1

x \to 0 lim (x^{3})

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

8 y^{^{''}} - 2 y^{^{'}} - y = 4 + 5 sin (2 t)

a re a y = x^{2} - 3 x, y = 2 x + 6