derivative of 2x^5-6x^4+4x^3+4x^2-6x+2

解

\frac{d}{d x} (2 x^{5} - 6 x^{4} + 4 x^{3} + 4 x^{2} - 6 x + 2)

10 x^{4} - 24 x^{3} + 12 x^{2} + 8 x - 6

解答ステップ

\frac{d}{d x} (2 x^{5} - 6 x^{4} + 4 x^{3} + 4 x^{2} - 6 x + 2)

和/差の法則を適用:

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

= \frac{d}{d x} (2 x^{5}) - \frac{d}{d x} (6 x^{4}) + \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (4 x^{2}) - \frac{d}{d x} (6 x) + \frac{d}{d x} (2)

\frac{d}{d x} (2 x^{5}) = 10 x^{4}

\frac{d}{d x} (6 x^{4}) = 24 x^{3}

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

\frac{d}{d x} (4 x^{2}) = 8 x

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

\frac{d}{d x} (2) = 0

= 10 x^{4} - 24 x^{3} + 12 x^{2} + 8 x - 6 + 0

簡素化

= 10 x^{4} - 24 x^{3} + 12 x^{2} + 8 x - 6