derivative arctan(x/5)

解答

导数

arctan (\frac{x}{5})

\frac{5}{x ^{2} + 25}

求解步骤

\frac{d}{d x} (arctan (\frac{x}{5}))

使用连锁律:

\frac{1}{( \frac{x}{5} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{5})

= \frac{1}{( \frac{x}{5} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= \frac{1}{( \frac{x}{5} ) ^{2} + 1} \cdot \frac{1}{5}

化简

\frac{1}{( \frac{x}{5} ) ^{2} + 1} \cdot \frac{1}{5} : \frac{5}{x ^{2} + 25}

= \frac{5}{x ^{2} + 25}

\int_{- 1}^{0} \frac{1}{x ^{3}} d x

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{6}{x ^{4}}) (x + 8 x^{3}))

x \to 1 lim (\frac{0}{x ^{2} - 1})

\int (18 x + 5) d x

\int 2 e^{3 x} d x