derivative (x^4+7x^2-9)^5

解

導関数

(x^{4} + 7 x^{2} - 9)^{5}

5 (x^{4} + 7 x^{2} - 9)^{4} (4 x^{3} + 14 x)

解答ステップ

\frac{d}{d x} ((x^{4} + 7 x^{2} - 9)^{5})

連鎖法則を適用:

5 (x^{4} + 7 x^{2} - 9)^{4} \frac{d}{d x} (x^{4} + 7 x^{2} - 9)

= 5 (x^{4} + 7 x^{2} - 9)^{4} \frac{d}{d x} (x^{4} + 7 x^{2} - 9)

\frac{d}{d x} (x^{4} + 7 x^{2} - 9) = 4 x^{3} + 14 x

= 5 (x^{4} + 7 x^{2} - 9)^{4} (4 x^{3} + 14 x)