derivative of (2x+1^4+8x(2x+1)^3)

解

\frac{d}{d x} ((2 x + 1)^{4} + 8 x (2 x + 1)^{3})

320 x^{3} + 384 x^{2} + 144 x + 16

解答ステップ

\frac{d}{d x} ((2 x + 1)^{4} + 8 x (2 x + 1)^{3})

簡素化

(2 x + 1)^{4} + 8 x (2 x + 1)^{3} : 80 x^{4} + 128 x^{3} + 72 x^{2} + 16 x + 1

= \frac{d}{d x} (80 x^{4} + 128 x^{3} + 72 x^{2} + 16 x + 1)

和/差の法則を適用:

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

= \frac{d}{d x} (80 x^{4}) + \frac{d}{d x} (128 x^{3}) + \frac{d}{d x} (72 x^{2}) + \frac{d}{d x} (16 x) + \frac{d}{d x} (1)

\frac{d}{d x} (80 x^{4}) = 320 x^{3}

\frac{d}{d x} (128 x^{3}) = 384 x^{2}

\frac{d}{d x} (72 x^{2}) = 144 x

\frac{d}{d x} (16 x) = 16

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

= 320 x^{3} + 384 x^{2} + 144 x + 16 + 0

簡素化

= 320 x^{3} + 384 x^{2} + 144 x + 16