(\partial)/(\partial x)((x^4+3x^2)(1-5x))

解

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

- 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x

解答ステップ

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

積の法則を適用:

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

f = x^{4} + 3 x^{2}, g = 1 - 5 x

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

\frac{\partial}{\partial x} (x^{4} + 3 x^{2}) = 4 x^{3} + 6 x

\frac{\partial}{\partial x} (1 - 5 x) = - 5

= (4 x^{3} + 6 x) (1 - 5 x) + (- 5) (x^{4} + 3 x^{2})

簡素化

(4 x^{3} + 6 x) (1 - 5 x) + (- 5) (x^{4} + 3 x^{2}) : - 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x

= - 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x