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

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

y^{^{''}} - 9 y^{^{'}} + 18 y = 0

d er i v a t i v e \frac{x}{y ^{13}} + B e^{y}

\int (csc^{4} (θ)) d θ

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\int \frac{2}{x ^{2} + 3 x - 4} d x