derivative f(x)=(5x^3+6x^2+4)^8

解

導関数

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

8 (5 x^{3} + 6 x^{2} + 4)^{7} (15 x^{2} + 12 x)

解答ステップ

\frac{d}{d x} ((5 x^{3} + 6 x^{2} + 4)^{8})

連鎖法則を適用:

8 (5 x^{3} + 6 x^{2} + 4)^{7} \frac{d}{d x} (5 x^{3} + 6 x^{2} + 4)

= 8 (5 x^{3} + 6 x^{2} + 4)^{7} \frac{d}{d x} (5 x^{3} + 6 x^{2} + 4)

\frac{d}{d x} (5 x^{3} + 6 x^{2} + 4) = 15 x^{2} + 12 x

= 8 (5 x^{3} + 6 x^{2} + 4)^{7} (15 x^{2} + 12 x)