derivative of 2x^3-15x^2+36x-10

解

\frac{d}{d x} (2 x^{3} - 15 x^{2} + 36 x - 10)

6 x^{2} - 30 x + 36

解答ステップ

\frac{d}{d x} (2 x^{3} - 15 x^{2} + 36 x - 10)

和/差の法則を適用:

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

= \frac{d}{d x} (2 x^{3}) - \frac{d}{d x} (15 x^{2}) + \frac{d}{d x} (36 x) - \frac{d}{d x} (10)

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (15 x^{2}) = 30 x

\frac{d}{d x} (36 x) = 36

\frac{d}{d x} (10) = 0

= 6 x^{2} - 30 x + 36 - 0

簡素化

= 6 x^{2} - 30 x + 36