derivative y=(2x+3)^5+10x(2x+3)^4

解

導関数

y = (2 x + 3)^{5} + 10 x (2 x + 3)^{4}

960 x^{4} + 4800 x^{3} + 8640 x^{2} + 6480 x + 1620

解答ステップ

\frac{d}{d x} ((2 x + 3)^{5} + 10 x (2 x + 3)^{4})

簡素化

(2 x + 3)^{5} + 10 x (2 x + 3)^{4} : 192 x^{5} + 1200 x^{4} + 2880 x^{3} + 3240 x^{2} + 1620 x + 243

= \frac{d}{d x} (192 x^{5} + 1200 x^{4} + 2880 x^{3} + 3240 x^{2} + 1620 x + 243)

和/差の法則を適用:

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

= \frac{d}{d x} (192 x^{5}) + \frac{d}{d x} (1200 x^{4}) + \frac{d}{d x} (2880 x^{3}) + \frac{d}{d x} (3240 x^{2}) + \frac{d}{d x} (1620 x) + \frac{d}{d x} (243)

\frac{d}{d x} (192 x^{5}) = 960 x^{4}

\frac{d}{d x} (1200 x^{4}) = 4800 x^{3}

\frac{d}{d x} (2880 x^{3}) = 8640 x^{2}

\frac{d}{d x} (3240 x^{2}) = 6480 x

\frac{d}{d x} (1620 x) = 1620

\frac{d}{d x} (243) = 0

= 960 x^{4} + 4800 x^{3} + 8640 x^{2} + 6480 x + 1620 + 0

簡素化

= 960 x^{4} + 4800 x^{3} + 8640 x^{2} + 6480 x + 1620