derivative f(x)=ln((sqrt(4+x^2))/x)

解答

导数

f (x) = ln (\frac{4 + x ^{2}}{x})

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

t an g e n t f (x) = 20 x, (4, 40)

y^{^{''}} + 5 y^{^{'}} - 2 y = 0

\int \frac{1}{t ^{2} - 12 t + 40} d t

x \to 0 - lim \frac{1}{\frac{1}{x}}

d er i v a t i v e (t^{6} + 26 t^{4} - t^{3} + 179)^{73}