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

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

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

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

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derivative of

f (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}}

\frac{d ^{4}}{d x ^{4}} (ln (1 - x))

\int_{1}^{2} \frac{5}{8 x ^{6}} d x

n = 2 \sum \infty \frac{1}{n - 1}

x y^{^{'}} + y = 3 x + 5 x

y = - 0, 7248 x 2 - 0, 2682 x + 0, 6271

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