derivative 3xsqrt(4x^2+4)

解

導関数

3 x 4 x^{2} + 4

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

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

積の法則を適用:

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

f = x, g = 4 x^{2} + 4

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

\frac{d x}{d x} = 1

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

= 3 (1 \cdot 4 x^{2} + 4 + \frac{2 x}{x ^{2} + 1} x)

簡素化

3 (1 \cdot 4 x^{2} + 4 + \frac{2 x}{x ^{2} + 1} x) : \frac{3 ( 4 x ^{2} + 2 )}{x ^{2} + 1}

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