derivative of 2xln(x+x^2-1)

解

\frac{d}{d x} (2 x ln (x) + x^{2} - 1)

2 x + 2 (ln (x) + 1)

解答ステップ

\frac{d}{d x} (2 x ln (x) + x^{2} - 1)

和/差の法則を適用:

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

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

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

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

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

= 2 (ln (x) + 1) + 2 x - 0

簡素化

= 2 x + 2 (ln (x) + 1)