derivative of (x/7+7/x ^7)

解答

\frac{d}{d x} ((\frac{x}{7} + \frac{7}{x})^{7})

(\frac{x}{7} + \frac{7}{x})^{6} - \frac{( x ^{2} + 49 ) ^{6}}{2401 x ^{8}}

求解步骤

\frac{d}{d x} ((\frac{x}{7} + \frac{7}{x})^{7})

使用连锁律:

7 (\frac{x}{7} + \frac{7}{x})^{6} \frac{d}{d x} (\frac{x}{7} + \frac{7}{x})

= 7 (\frac{x}{7} + \frac{7}{x})^{6} \frac{d}{d x} (\frac{x}{7} + \frac{7}{x})

\frac{d}{d x} (\frac{x}{7} + \frac{7}{x}) = \frac{1}{7} - \frac{7}{x ^{2}}

= 7 (\frac{x}{7} + \frac{7}{x})^{6} (\frac{1}{7} - \frac{7}{x ^{2}})

化简

7 (\frac{x}{7} + \frac{7}{x})^{6} (\frac{1}{7} - \frac{7}{x ^{2}}) : (\frac{x}{7} + \frac{7}{x})^{6} - \frac{( x ^{2} + 49 ) ^{6}}{2401 x ^{8}}

= (\frac{x}{7} + \frac{7}{x})^{6} - \frac{( x ^{2} + 49 ) ^{6}}{2401 x ^{8}}

\int \frac{1}{3 x ^{2} - 1} d x

i = 2 \sum \infty \frac{5}{i ^{2} + i - 2}

x \to 5 lim (2 x + 3)

l a pl a ce t r an s f or m 3 \cdot cos^{2} (t)

x^{^{'}} = 0.0333333 x (30 - x)