derivative f(x)=arctan(2/x)

解答

导数

f (x) = arctan (\frac{2}{x})

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

求解步骤

\frac{d}{d x} (arctan (\frac{2}{x}))

使用连锁律:

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

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

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

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

化简

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

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

\int x \cdot cos (k x) d x

t an g e n t - 10 x^{4} + x^{3}

d er i v a t i v e y = x^{\frac{13}{14}}

n = 1 \sum \infty ln ((n + 1)^{2})

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 4