(\partial)/(\partial x)((r)(a(cos(x)+1)))

解

\frac{\partial}{\partial x} ((r) (a (cos (x) + 1)))

- a r sin (x)

解答ステップ

\frac{\partial}{\partial x} ((r) (a (cos (x) + 1)))

a, r

を定数として扱う

定数を除去:

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

= r a \frac{\partial}{\partial x} (cos (x) + 1)

和/差の法則を適用:

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

= r a (\frac{\partial}{\partial x} (cos (x)) + \frac{\partial}{\partial x} (1))

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

\frac{\partial}{\partial x} (1) = 0

= r a (- sin (x) + 0)

簡素化

= - a r sin (x)