derivative of (5+3xcos(x))

解

\frac{d}{d x} ((5 + 3 x) cos (x))

3 cos (x) - sin (x) (5 + 3 x)

解答ステップ

\frac{d}{d x} ((5 + 3 x) cos (x))

積の法則を適用:

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

f = 5 + 3 x, g = cos (x)

= \frac{d}{d x} (5 + 3 x) cos (x) + \frac{d}{d x} (cos (x)) (5 + 3 x)

\frac{d}{d x} (5 + 3 x) = 3

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

= 3 cos (x) + (- sin (x)) (5 + 3 x)

簡素化

= 3 cos (x) - sin (x) (5 + 3 x)