derivative of x^6-4x^5+5x^4-5x^2+4x-1

解

\frac{d}{d x} (x^{6} - 4 x^{5} + 5 x^{4} - 5 x^{2} + 4 x - 1)

6 x^{5} - 20 x^{4} + 20 x^{3} - 10 x + 4

解答ステップ

\frac{d}{d x} (x^{6} - 4 x^{5} + 5 x^{4} - 5 x^{2} + 4 x - 1)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{6}) - \frac{d}{d x} (4 x^{5}) + \frac{d}{d x} (5 x^{4}) - \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (4 x) - \frac{d}{d x} (1)

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (4 x^{5}) = 20 x^{4}

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

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

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

\frac{d}{d x} (1) = 0

= 6 x^{5} - 20 x^{4} + 20 x^{3} - 10 x + 4 - 0

簡素化

= 6 x^{5} - 20 x^{4} + 20 x^{3} - 10 x + 4