derivative ln(1+x^2)

解答

导数

ln (1 + x^{2})

\frac{2 x}{1 + x ^{2}}

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

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