derivative of xsqrt(3+x^2)

解

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

\frac{2 x ^{2} + 3}{3 + x ^{2}}

解答ステップ

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

積の法則を適用:

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

f = x, g = 3 + x^{2}

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

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

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

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

簡素化

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

= \frac{2 x ^{2} + 3}{3 + x ^{2}}