derivative of (-x^3-x^2+xcos(x))

解

\frac{d}{d x} ((- x^{3} - x^{2} + x) cos (x))

cos (x) (- 3 x^{2} - 2 x + 1) - sin (x) (- x^{3} - x^{2} + x)

解答ステップ

\frac{d}{d x} ((- x^{3} - x^{2} + x) cos (x))

積の法則を適用:

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

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

= \frac{d}{d x} (- x^{3} - x^{2} + x) cos (x) + \frac{d}{d x} (cos (x)) (- x^{3} - x^{2} + x)

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

\frac{d}{d x} (cos (x)) = - sin (x)

= (- 3 x^{2} - 2 x + 1) cos (x) + (- sin (x)) (- x^{3} - x^{2} + x)

簡素化

= cos (x) (- 3 x^{2} - 2 x + 1) - sin (x) (- x^{3} - x^{2} + x)