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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derivative of

(\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 [x^{2} cos (x)] d x

\frac{d}{d x} (9 x^{8} e^{x} + e^{x x^{9}})

\frac{y ^{4}}{4} + \frac{1}{8 y ^{2}}

\int_{1}^{4} - 9 e^{x} d x

(- 3, 7), (2, - 6)

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)