derivative of (x^3-5^5(x^5+7))

解

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

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

解答ステップ

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

積の法則を適用:

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

f = (x^{3} - 5)^{5}, g = x^{5} + 7

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

\frac{d}{d x} ((x^{3} - 5)^{5}) = 15 x^{2} (x^{3} - 5)^{4}

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

= 15 x^{2} (x^{3} - 5)^{4} (x^{5} + 7) + 5 x^{4} (x^{3} - 5)^{5}