derivative f(x)=(-9x^3+2x^2)^5

解

導関数

f (x) = (- 9 x^{3} + 2 x^{2})^{5}

5 (- 9 x^{3} + 2 x^{2})^{4} (- 27 x^{2} + 4 x)

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (- 9 x^{3} + 2 x^{2}) = - 27 x^{2} + 4 x

= 5 (- 9 x^{3} + 2 x^{2})^{4} (- 27 x^{2} + 4 x)