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

解

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

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

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= (2 x + 1) cos (5 x) + (- sin (5 x) \cdot 5) (x^{2} + x)

簡素化

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