derivative 15x^{100}-3x^{12}+5x-46

解

導関数

15 x^{100} - 3 x^{12} + 5 x - 46

1500 x^{99} - 36 x^{11} + 5

解答ステップ

\frac{d}{d x} (15 x^{100} - 3 x^{12} + 5 x - 46)

和/差の法則を適用:

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

= \frac{d}{d x} (15 x^{100}) - \frac{d}{d x} (3 x^{12}) + \frac{d}{d x} (5 x) - \frac{d}{d x} (46)

\frac{d}{d x} (15 x^{100}) = 1500 x^{99}

\frac{d}{d x} (3 x^{12}) = 36 x^{11}

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

\frac{d}{d x} (46) = 0

= 1500 x^{99} - 36 x^{11} + 5 - 0

簡素化

= 1500 x^{99} - 36 x^{11} + 5