derivative ln(xsqrt(x^2-1))

解答

导数

ln (x x^{2} - 1)

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

s l o p e (- 3, - 2), (1, - 5)

\int cos (x) (1 + 7 sin^{2} (x)) d x

n = 0 \sum \infty \frac{1}{n ^{4} + 6}

t an g e n t f (x) = x, at x = 5

f^{^{''}} (t) - f (t) = - 8 t, f (3) = - 8