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

解

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

(x^{5} + 5)^{3} + 15 x^{5} (x^{5} + 5)^{2}

解答ステップ

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

積の法則を適用:

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

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

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

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

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

= 1 \cdot (x^{5} + 5)^{3} + 15 x^{4} (x^{5} + 5)^{2} x

簡素化

1 \cdot (x^{5} + 5)^{3} + 15 x^{4} (x^{5} + 5)^{2} x : (x^{5} + 5)^{3} + 15 x^{5} (x^{5} + 5)^{2}

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