(\partial)/(\partial y)(y^2cos(y))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = y^{2}, g = cos (y)

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

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

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

= 2 y cos (y) + (- sin (y)) y^{2}

Vereinfache

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

x \to 3 lim (\frac{x ^{2} + 1}{x - 2})

d er i v a t i v e f (x) = (x^{3} + 5) e^{x}

y^{^{''}} + 10 y^{^{'}} + 21 y = 0

d er i v a t i v e (9 x + 2)^{\frac{2}{3}}

\int (4 x + 2) (x - 1) d x