derivative of (3x^2-5x^9(-2x^4+2x-8)^4)

解

\frac{d}{d x} ((3 x^{2} - 5 x)^{9} (- 2 x^{4} + 2 x - 8)^{4})

9 (3 x^{2} - 5 x)^{8} (6 x - 5) (- 2 x^{4} + 2 x - 8)^{4} + 4 (- 2 x^{4} + 2 x - 8)^{3} (- 8 x^{3} + 2) (3 x^{2} - 5 x)^{9}

解答ステップ

\frac{d}{d x} ((3 x^{2} - 5 x)^{9} (- 2 x^{4} + 2 x - 8)^{4})

積の法則を適用:

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

f = (3 x^{2} - 5 x)^{9}, g = (- 2 x^{4} + 2 x - 8)^{4}

= \frac{d}{d x} ((3 x^{2} - 5 x)^{9}) (- 2 x^{4} + 2 x - 8)^{4} + \frac{d}{d x} ((- 2 x^{4} + 2 x - 8)^{4}) (3 x^{2} - 5 x)^{9}

\frac{d}{d x} ((3 x^{2} - 5 x)^{9}) = 9 (3 x^{2} - 5 x)^{8} (6 x - 5)

\frac{d}{d x} ((- 2 x^{4} + 2 x - 8)^{4}) = 4 (- 2 x^{4} + 2 x - 8)^{3} (- 8 x^{3} + 2)

= 9 (3 x^{2} - 5 x)^{8} (6 x - 5) (- 2 x^{4} + 2 x - 8)^{4} + 4 (- 2 x^{4} + 2 x - 8)^{3} (- 8 x^{3} + 2) (3 x^{2} - 5 x)^{9}