derivative y=(x^6-7x+4)(x^4-5x)

解

導関数

y = (x^{6} - 7 x + 4) (x^{4} - 5 x)

10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20

解答ステップ

\frac{d}{d x} ((x^{6} - 7 x + 4) (x^{4} - 5 x))

積の法則を適用:

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

f = x^{6} - 7 x + 4, g = x^{4} - 5 x

= \frac{d}{d x} (x^{6} - 7 x + 4) (x^{4} - 5 x) + \frac{d}{d x} (x^{4} - 5 x) (x^{6} - 7 x + 4)

\frac{d}{d x} (x^{6} - 7 x + 4) = 6 x^{5} - 7

\frac{d}{d x} (x^{4} - 5 x) = 4 x^{3} - 5

= (6 x^{5} - 7) (x^{4} - 5 x) + (4 x^{3} - 5) (x^{6} - 7 x + 4)

簡素化

(6 x^{5} - 7) (x^{4} - 5 x) + (4 x^{3} - 5) (x^{6} - 7 x + 4) : 10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20

= 10 x^{9} - 35 x^{6} - 35 x^{4} + 16 x^{3} + 70 x - 20