derivative of x^3-12x^2+45x+9

解

\frac{d}{d x} (x^{3} - 12 x^{2} + 45 x + 9)

3 x^{2} - 24 x + 45

解答ステップ

\frac{d}{d x} (x^{3} - 12 x^{2} + 45 x + 9)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (12 x^{2}) + \frac{d}{d x} (45 x) + \frac{d}{d x} (9)

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (12 x^{2}) = 24 x

\frac{d}{d x} (45 x) = 45

\frac{d}{d x} (9) = 0

= 3 x^{2} - 24 x + 45 + 0

簡素化

= 3 x^{2} - 24 x + 45