derivative 400x^{10}+40x^5+1

解

導関数

400 x^{10} + 40 x^{5} + 1

4000 x^{9} + 200 x^{4}

解答ステップ

\frac{d}{d x} (400 x^{10} + 40 x^{5} + 1)

和/差の法則を適用:

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

= \frac{d}{d x} (400 x^{10}) + \frac{d}{d x} (40 x^{5}) + \frac{d}{d x} (1)

\frac{d}{d x} (400 x^{10}) = 4000 x^{9}

\frac{d}{d x} (40 x^{5}) = 200 x^{4}

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

= 4000 x^{9} + 200 x^{4} + 0

簡素化

= 4000 x^{9} + 200 x^{4}