derivative of ln(x+sqrt(4+x^2))

解答

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

\frac{1}{4 + x ^{2}}

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

= \frac{1}{4 + x ^{2}}

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