derivative y=x(x^3+7)^4

解

導関数

y = x (x^{3} + 7)^{4}

(x^{3} + 7)^{4} + 12 x^{3} (x^{3} + 7)^{3}

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x^{3} + 7)^{4}

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

\frac{d x}{d x} = 1

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

= 1 \cdot (x^{3} + 7)^{4} + 12 x^{2} (x^{3} + 7)^{3} x

簡素化

1 \cdot (x^{3} + 7)^{4} + 12 x^{2} (x^{3} + 7)^{3} x : (x^{3} + 7)^{4} + 12 x^{3} (x^{3} + 7)^{3}

= (x^{3} + 7)^{4} + 12 x^{3} (x^{3} + 7)^{3}