(\partial)/(\partial x)(log_{3}(7^{x^2-4}))

解

\frac{\partial}{\partial x} (lo g_{3} (7^{x^{2} - 4}))

2 lo g_{3} (7) x

解答ステップ

\frac{\partial}{\partial x} (lo g_{3} (7^{x^{2} - 4}))

簡素化

lo g_{3} (7^{x^{2} - 4}) : lo g_{3} (7) (x^{2} - 4)

= \frac{\partial}{\partial x} (lo g_{3} (7) (x^{2} - 4))

定数を除去:

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

= lo g_{3} (7) \frac{\partial}{\partial x} (x^{2} - 4)

和/差の法則を適用:

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

= lo g_{3} (7) (\frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (4))

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

\frac{\partial}{\partial x} (4) = 0

= lo g_{3} (7) (2 x - 0)

簡素化

= 2 lo g_{3} (7) x