derivative F(x)=(7x^6+4x^3)^4

解

導関数

F (x) = (7 x^{6} + 4 x^{3})^{4}

4 (7 x^{6} + 4 x^{3})^{3} (42 x^{5} + 12 x^{2})

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (7 x^{6} + 4 x^{3}) = 42 x^{5} + 12 x^{2}

= 4 (7 x^{6} + 4 x^{3})^{3} (42 x^{5} + 12 x^{2})