derivative y=3sin(x^3-5x^2+8x+0.5)

解

導関数

y = 3 sin (x^{3} - 5 x^{2} + 8 x + 0.5)

3 cos (x^{3} - 5 x^{2} + 8 x + 0.5) (3 x^{2} - 10 x + 8)

解答ステップ

\frac{d}{d x} (3 sin (x^{3} - 5 x^{2} + 8 x + 0.5))

定数を除去:

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

= 3 \frac{d}{d x} (sin (x^{3} - 5 x^{2} + 8 x + 0.5))

連鎖法則を適用:

cos (x^{3} - 5 x^{2} + 8 x + 0.5) \frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5)

= cos (x^{3} - 5 x^{2} + 8 x + 0.5) \frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5)

\frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5) = 3 x^{2} - 10 x + 8

= 3 cos (x^{3} - 5 x^{2} + 8 x + 0.5) (3 x^{2} - 10 x + 8)