derivative of x^7cos(x)

解

\frac{d}{d x} (x^{7} cos (x))

7 x^{6} cos (x) - x^{7} sin (x)

解答ステップ

\frac{d}{d x} (x^{7} cos (x))

積の法則を適用:

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

f = x^{7}, g = cos (x)

= \frac{d}{d x} (x^{7}) cos (x) + \frac{d}{d x} (cos (x)) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} cos (x) + (- sin (x)) x^{7}

簡素化

= 7 x^{6} cos (x) - x^{7} sin (x)