derivative of (x-100^3+(x-100)^2+500)

解

\frac{d}{d x} ((x - 100)^{3} + (x - 100)^{2} + 500)

3 x^{2} - 598 x + 29800

解答ステップ

\frac{d}{d x} ((x - 100)^{3} + (x - 100)^{2} + 500)

簡素化

(x - 100)^{3} + (x - 100)^{2} + 500 : x^{3} - 299 x^{2} + 29800 x - 989500

= \frac{d}{d x} (x^{3} - 299 x^{2} + 29800 x - 989500)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (299 x^{2}) + \frac{d}{d x} (29800 x) - \frac{d}{d x} (989500)

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

\frac{d}{d x} (299 x^{2}) = 598 x

\frac{d}{d x} (29800 x) = 29800

\frac{d}{d x} (989500) = 0

= 3 x^{2} - 598 x + 29800 - 0

簡素化

= 3 x^{2} - 598 x + 29800