derivative 5x^4-28x^3+42x^2-196x+49

解

導関数

5 x^{4} - 28 x^{3} + 42 x^{2} - 196 x + 49

20 x^{3} - 84 x^{2} + 84 x - 196

解答ステップ

\frac{d}{d x} (5 x^{4} - 28 x^{3} + 42 x^{2} - 196 x + 49)

和/差の法則を適用:

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

= \frac{d}{d x} (5 x^{4}) - \frac{d}{d x} (28 x^{3}) + \frac{d}{d x} (42 x^{2}) - \frac{d}{d x} (196 x) + \frac{d}{d x} (49)

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

\frac{d}{d x} (28 x^{3}) = 84 x^{2}

\frac{d}{d x} (42 x^{2}) = 84 x

\frac{d}{d x} (196 x) = 196

\frac{d}{d x} (49) = 0

= 20 x^{3} - 84 x^{2} + 84 x - 196 + 0

簡素化

= 20 x^{3} - 84 x^{2} + 84 x - 196