derivative of (3x+5^3-5x)

解

\frac{d}{d x} ((3 x + 5)^{3} - 5 x)

81 x^{2} + 270 x + 220

解答ステップ

\frac{d}{d x} ((3 x + 5)^{3} - 5 x)

簡素化

(3 x + 5)^{3} - 5 x : 27 x^{3} + 135 x^{2} + 220 x + 125

= \frac{d}{d x} (27 x^{3} + 135 x^{2} + 220 x + 125)

和/差の法則を適用:

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

= \frac{d}{d x} (27 x^{3}) + \frac{d}{d x} (135 x^{2}) + \frac{d}{d x} (220 x) + \frac{d}{d x} (125)

\frac{d}{d x} (27 x^{3}) = 81 x^{2}

\frac{d}{d x} (135 x^{2}) = 270 x

\frac{d}{d x} (220 x) = 220

\frac{d}{d x} (125) = 0

= 81 x^{2} + 270 x + 220 + 0

簡素化

= 81 x^{2} + 270 x + 220