derivative of arcsin(xln(x))

解答

\frac{d}{d x} (arcsin (x ln (x)))

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

求解步骤

\frac{d}{d x} (arcsin (x ln (x)))

使用连锁律:

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

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

\frac{d}{d x} (x ln (x)) = ln (x) + 1

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

化简

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

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

\int_{0}^{1} \frac{5}{1 + x ^{2}} d x

(1 + \frac{y}{x ^{2}}) d x - \frac{1}{x} d y = 0

\frac{\partial}{\partial x} (\frac{x ^{2}}{2 y})

\frac{d}{d x} (- \frac{1}{4 sin ( x )})

\frac{1}{- 0.75 y - 0.00003} y^{^{'}} = 1