derivative of 3x^5-4x^4+9x-6

解

\frac{d}{d x} (3 x^{5} - 4 x^{4} + 9 x - 6)

15 x^{4} - 16 x^{3} + 9

解答ステップ

\frac{d}{d x} (3 x^{5} - 4 x^{4} + 9 x - 6)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x^{5}) - \frac{d}{d x} (4 x^{4}) + \frac{d}{d x} (9 x) - \frac{d}{d x} (6)

\frac{d}{d x} (3 x^{5}) = 15 x^{4}

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

\frac{d}{d x} (9 x) = 9

\frac{d}{d x} (6) = 0

= 15 x^{4} - 16 x^{3} + 9 - 0

簡素化

= 15 x^{4} - 16 x^{3} + 9