(\partial)/(\partial x)((2x^2-5x)^3(2x+1))

解

\frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3} (2 x + 1))

3 (2 x^{2} - 5 x)^{2} (4 x - 5) (2 x + 1) + 2 (2 x^{2} - 5 x)^{3}

解答ステップ

\frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3} (2 x + 1))

積の法則を適用:

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

f = (2 x^{2} - 5 x)^{3}, g = 2 x + 1

= \frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3}) (2 x + 1) + \frac{\partial}{\partial x} (2 x + 1) (2 x^{2} - 5 x)^{3}

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

\frac{\partial}{\partial x} (2 x + 1) = 2

= 3 (2 x^{2} - 5 x)^{2} (4 x - 5) (2 x + 1) + 2 (2 x^{2} - 5 x)^{3}