derivative of ({P}(x)(x(36-x)^2))

解

\frac{d}{d x} ((P (x)) (x (36 - x)^{2}))

\frac{d}{d x} (P (x)) x (36 - x)^{2} + (3 x^{2} - 144 x + 1296) P (x)

解答ステップ

\frac{d}{d x} ((P (x)) (x (36 - x)^{2}))

積の法則を適用:

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

f = P (x), g = x (36 - x)^{2}

= \frac{d}{d x} (P (x)) x (36 - x)^{2} + \frac{d}{d x} (x (36 - x)^{2}) P (x)

\frac{d}{d x} (x (36 - x)^{2}) = 3 x^{2} - 144 x + 1296

= \frac{d}{d x} (P (x)) x (36 - x)^{2} + (3 x^{2} - 144 x + 1296) P (x)