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}}

\int_{0}^{1} x e^{x} d x

x y y^{^{'}} = (y^{2} - 1)^{\frac{3}{2}}

\frac{\partial}{\partial y} (x yz + x y^{5} + y z^{5} + z x^{5})

\int_{0}^{1} cos^{2} (2 π x) d x

\frac{d}{d x} (x^{0.5} + 2 x^{- 0.5})

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)