derivative of ln(xsqrt(x^2-6))

解答

\frac{d}{d x} (ln (x x^{2} - 6))

\frac{2 x ^{2} - 6}{x ( x ^{2} - 6 )}

求解步骤

\frac{d}{d x} (ln (x x^{2} - 6))

使用连锁律:

\frac{1}{x x ^{2} - 6} \frac{d}{d x} (x x^{2} - 6)

= \frac{1}{x x ^{2} - 6} \frac{d}{d x} (x x^{2} - 6)

\frac{d}{d x} (x x^{2} - 6) = \frac{2 x ^{2} - 6}{x ^{2} - 6}

= \frac{1}{x x ^{2} - 6} \cdot \frac{2 x ^{2} - 6}{x ^{2} - 6}

化简

\frac{1}{x x ^{2} - 6} \cdot \frac{2 x ^{2} - 6}{x ^{2} - 6} : \frac{2 x ^{2} - 6}{x ( x ^{2} - 6 )}

= \frac{2 x ^{2} - 6}{x ( x ^{2} - 6 )}

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