(\partial)/(\partial x)(3xy^2+2ycos(x))

解

\frac{\partial}{\partial x} (3 x y^{2} + 2 y cos (x))

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

解答ステップ

\frac{\partial}{\partial x} (3 x y^{2} + 2 y cos (x))

y

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial x} (3 x y^{2}) + \frac{\partial}{\partial x} (2 y cos (x))

\frac{\partial}{\partial x} (3 x y^{2}) = 3 y^{2}

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

= 3 y^{2} - 2 y sin (x)