derivative of (5x-3(2x+5)^2)

解

\frac{d}{d x} ((5 x - 3) (2 x + 5)^{2})

60 x^{2} + 176 x + 65

解答ステップ

\frac{d}{d x} ((5 x - 3) (2 x + 5)^{2})

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 5 x - 3, g = (2 x + 5)^{2}

= \frac{d}{d x} (5 x - 3) (2 x + 5)^{2} + \frac{d}{d x} ((2 x + 5)^{2}) (5 x - 3)

\frac{d}{d x} (5 x - 3) = 5

\frac{d}{d x} ((2 x + 5)^{2}) = 4 (2 x + 5)

= 5 (2 x + 5)^{2} + 4 (2 x + 5) (5 x - 3)

簡素化

5 (2 x + 5)^{2} + 4 (2 x + 5) (5 x - 3) : 60 x^{2} + 176 x + 65

= 60 x^{2} + 176 x + 65