derivative of x^2(x+sin(x)^5)

解

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

2 x (x + sin (x))^{5} + 5 (x + sin (x))^{4} (1 + cos (x)) x^{2}

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = (x + sin (x))^{5}

= \frac{d}{d x} (x^{2}) (x + sin (x))^{5} + \frac{d}{d x} ((x + sin (x))^{5}) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} ((x + sin (x))^{5}) = 5 (x + sin (x))^{4} (1 + cos (x))

= 2 x (x + sin (x))^{5} + 5 (x + sin (x))^{4} (1 + cos (x)) x^{2}