derivative (x^2+9)^2(x-9)

解

導関数

(x^{2} + 9)^{2} (x - 9)

5 x^{4} - 36 x^{3} + 54 x^{2} - 324 x + 81

解答ステップ

\frac{d}{d x} ((x^{2} + 9)^{2} (x - 9))

積の法則を適用:

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

f = (x^{2} + 9)^{2}, g = x - 9

= \frac{d}{d x} ((x^{2} + 9)^{2}) (x - 9) + \frac{d}{d x} (x - 9) (x^{2} + 9)^{2}

\frac{d}{d x} ((x^{2} + 9)^{2}) = 4 x (x^{2} + 9)

\frac{d}{d x} (x - 9) = 1

= 4 x (x^{2} + 9) (x - 9) + 1 \cdot (x^{2} + 9)^{2}

簡素化

4 x (x^{2} + 9) (x - 9) + 1 \cdot (x^{2} + 9)^{2} : 5 x^{4} - 36 x^{3} + 54 x^{2} - 324 x + 81

= 5 x^{4} - 36 x^{3} + 54 x^{2} - 324 x + 81