derivative sqrt(ln(x^2+1))

解答

导数

ln (x^{2} + 1)

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

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

y^{^{'}} = \frac{x e ^{y}}{y}

t^{2} y^{^{''}} - 4 t y^{^{'}} + 6 y = 0

x \to 0 lim (\frac{2 x}{2 x ^{2}})

\int_{3}^{5} e^{6 x} d x