derivative f(x)=-3x^5cos(x)

解

導関数

f (x) = - 3 x^{5} cos (x)

- 3 (5 x^{4} cos (x) - x^{5} sin (x))

解答ステップ

\frac{d}{d x} (- 3 x^{5} cos (x))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

積の法則を適用:

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

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= - 3 (5 x^{4} cos (x) + (- sin (x)) x^{5})

簡素化

= - 3 (5 x^{4} cos (x) - x^{5} sin (x))