What is the derivative of (x/7+7/x ^7) ?

The derivative of (x/7+7/x ^7) is (x/7+7/x)^6-((x^2+49)^6)/(2401x^8)

What is the first derivative of (x/7+7/x ^7) ?

The first derivative of (x/7+7/x ^7) is (x/7+7/x)^6-((x^2+49)^6)/(2401x^8)

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\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}}

Solution steps

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

Apply the chain rule:

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}})

Simplify

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)

3 \cdot cos^{2} (t)

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

What is the derivative of (x/7+7/x ^7) ?
The derivative of (x/7+7/x ^7) is (x/7+7/x)^6-((x^2+49)^6)/(2401x^8)
What is the first derivative of (x/7+7/x ^7) ?
The first derivative of (x/7+7/x ^7) is (x/7+7/x)^6-((x^2+49)^6)/(2401x^8)