What is the derivative of (x^5-6/x ^{-2}) ?

The derivative of (x^5-6/x ^{-2}) is -(2x(5x^6+6))/((x^6-6)^3)

What is the first derivative of (x^5-6/x ^{-2}) ?

The first derivative of (x^5-6/x ^{-2}) is -(2x(5x^6+6))/((x^6-6)^3)

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\frac{d}{d x} ((x^{5} - \frac{6}{x})^{- 2})

- \frac{2 x ( 5 x ^{6} + 6 )}{( x ^{6} - 6 ) ^{3}}

Solution steps

\frac{d}{d x} ((x^{5} - \frac{6}{x})^{- 2})

Apply the chain rule:

- \frac{2}{( x ^{5} - \frac{6}{x} ) ^{3}} \frac{d}{d x} (x^{5} - \frac{6}{x})

= - \frac{2}{( x ^{5} - \frac{6}{x} ) ^{3}} \frac{d}{d x} (x^{5} - \frac{6}{x})

\frac{d}{d x} (x^{5} - \frac{6}{x}) = 5 x^{4} + \frac{6}{x ^{2}}

= - \frac{2}{( x ^{5} - \frac{6}{x} ) ^{3}} (5 x^{4} + \frac{6}{x ^{2}})

Simplify

- \frac{2}{( x ^{5} - \frac{6}{x} ) ^{3}} (5 x^{4} + \frac{6}{x ^{2}}) : - \frac{2 x ( 5 x ^{6} + 6 )}{( x ^{6} - 6 ) ^{3}}

= - \frac{2 x ( 5 x ^{6} + 6 )}{( x ^{6} - 6 ) ^{3}}

What is the derivative of (x^5-6/x ^{-2}) ?
The derivative of (x^5-6/x ^{-2}) is -(2x(5x^6+6))/((x^6-6)^3)
What is the first derivative of (x^5-6/x ^{-2}) ?
The first derivative of (x^5-6/x ^{-2}) is -(2x(5x^6+6))/((x^6-6)^3)