derivative (x)^4cos(7x-5)

解

導関数

(x)^{4} cos (7 x - 5)

4 x^{3} cos (7 x - 5) - 7 x^{4} sin (7 x - 5)

解答ステップ

\frac{d}{d x} (x^{4} cos (7 x - 5))

積の法則を適用:

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

f = x^{4}, g = cos (7 x - 5)

= \frac{d}{d x} (x^{4}) cos (7 x - 5) + \frac{d}{d x} (cos (7 x - 5)) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (cos (7 x - 5)) = - sin (7 x - 5) \cdot 7

= 4 x^{3} cos (7 x - 5) + (- sin (7 x - 5) \cdot 7) x^{4}

簡素化

= 4 x^{3} cos (7 x - 5) - 7 x^{4} sin (7 x - 5)