derivative f(x)=x^{14}cos(x)

解

導関数

f (x) = x^{14} cos (x)

14 x^{13} cos (x) - x^{14} sin (x)

解答ステップ

\frac{d}{d x} (x^{14} cos (x))

積の法則を適用:

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

f = x^{14}, g = cos (x)

= \frac{d}{d x} (x^{14}) cos (x) + \frac{d}{d x} (cos (x)) x^{14}

\frac{d}{d x} (x^{14}) = 14 x^{13}

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

= 14 x^{13} cos (x) + (- sin (x)) x^{14}

簡素化

= 14 x^{13} cos (x) - x^{14} sin (x)