derivative f(x)=(x^3+7x^2+5)^5

解

導関数

f (x) = (x^{3} + 7 x^{2} + 5)^{5}

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

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (x^{3} + 7 x^{2} + 5) = 3 x^{2} + 14 x

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