(\partial)/(\partial x)(I(x,c,t)n(3x+3ct))

解

\frac{\partial}{\partial x} (I (x, c, t) n (3 x + 3 c t))

n (\frac{\partial}{\partial x} (I (x, c, t)) (3 x + 3 c t) + 3 I (x, c, t))

解答ステップ

\frac{\partial}{\partial x} (I (x, c, t) n (3 x + 3 c t))

n, c, t

を定数として扱う

定数を除去:

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

= n \frac{\partial}{\partial x} (I (x, c, t) (3 x + 3 c t))

積の法則を適用:

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

f = I (x, c, t), g = 3 x + 3 c t

= n (\frac{\partial}{\partial x} (I (x, c, t)) (3 x + 3 c t) + \frac{\partial}{\partial x} (3 x + 3 c t) I (x, c, t))

\frac{\partial}{\partial x} (3 x + 3 c t) = 3

= n (\frac{\partial}{\partial x} (I (x, c, t)) (3 x + 3 c t) + 3 I (x, c, t))