What is the derivative of ((x+1/x)^{3/7}) ?

The derivative of ((x+1/x)^{3/7}) is -3/(7x^{10/7)(x+1)^{4/7}}

What is the first derivative of ((x+1/x)^{3/7}) ?

The first derivative of ((x+1/x)^{3/7}) is -3/(7x^{10/7)(x+1)^{4/7}}

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\frac{d}{d x} ((\frac{x + 1}{x})^{\frac{3}{7}})

- \frac{3}{7 x ^{\frac{10}{7}} ( x + 1 ) ^{\frac{4}{7}}}

Solution steps

\frac{d}{d x} ((\frac{x + 1}{x})^{\frac{3}{7}})

Apply the chain rule:

\frac{3}{7 ( \frac{x + 1}{x} ) ^{\frac{4}{7}}} \frac{d}{d x} (\frac{x + 1}{x})

= \frac{3}{7 ( \frac{x + 1}{x} ) ^{\frac{4}{7}}} \frac{d}{d x} (\frac{x + 1}{x})

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

= \frac{3}{7 ( \frac{x + 1}{x} ) ^{\frac{4}{7}}} (- \frac{1}{x ^{2}})

Simplify

\frac{3}{7 ( \frac{x + 1}{x} ) ^{\frac{4}{7}}} (- \frac{1}{x ^{2}}) : - \frac{3}{7 x ^{\frac{10}{7}} ( x + 1 ) ^{\frac{4}{7}}}

= - \frac{3}{7 x ^{\frac{10}{7}} ( x + 1 ) ^{\frac{4}{7}}}

What is the derivative of ((x+1/x)^{3/7}) ?
The derivative of ((x+1/x)^{3/7}) is -3/(7x^{10/7)(x+1)^{4/7}}
What is the first derivative of ((x+1/x)^{3/7}) ?
The first derivative of ((x+1/x)^{3/7}) is -3/(7x^{10/7)(x+1)^{4/7}}