(\partial)/(\partial x)(({f}(x))(x-2)^2)

解

\frac{\partial}{\partial x} ((f (x)) (x - 2)^{2})

\frac{\partial}{\partial x} (f (x)) (x - 2)^{2} + 2 (x - 2) f (x)

解答ステップ

\frac{\partial}{\partial x} ((f (x)) (x - 2)^{2})

積の法則を適用:

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

f = f (x), g = (x - 2)^{2}

= \frac{\partial}{\partial x} (f (x)) (x - 2)^{2} + \frac{\partial}{\partial x} ((x - 2)^{2}) f (x)

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

= \frac{\partial}{\partial x} (f (x)) (x - 2)^{2} + 2 (x - 2) f (x)