derivative (x^2-16x+64)(x^2+64x+4)

解

導関数

(x^{2} - 16 x + 64) (x^{2} + 64 x + 4)

4 x^{3} + 144 x^{2} - 1912 x + 4032

解答ステップ

\frac{d}{d x} ((x^{2} - 16 x + 64) (x^{2} + 64 x + 4))

積の法則を適用:

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

f = x^{2} - 16 x + 64, g = x^{2} + 64 x + 4

= \frac{d}{d x} (x^{2} - 16 x + 64) (x^{2} + 64 x + 4) + \frac{d}{d x} (x^{2} + 64 x + 4) (x^{2} - 16 x + 64)

\frac{d}{d x} (x^{2} - 16 x + 64) = 2 x - 16

\frac{d}{d x} (x^{2} + 64 x + 4) = 2 x + 64

= (2 x - 16) (x^{2} + 64 x + 4) + (2 x + 64) (x^{2} - 16 x + 64)

簡素化

(2 x - 16) (x^{2} + 64 x + 4) + (2 x + 64) (x^{2} - 16 x + 64) : 4 x^{3} + 144 x^{2} - 1912 x + 4032

= 4 x^{3} + 144 x^{2} - 1912 x + 4032