derivative of x^4-4x^3+3x^2-3

解

\frac{d}{d x} (x^{4} - 4 x^{3} + 3 x^{2} - 3)

4 x^{3} - 12 x^{2} + 6 x

解答ステップ

\frac{d}{d x} (x^{4} - 4 x^{3} + 3 x^{2} - 3)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (3)

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (3) = 0

= 4 x^{3} - 12 x^{2} + 6 x - 0

簡素化

= 4 x^{3} - 12 x^{2} + 6 x