What is the derivative of sqrt(2x-1/(x^2)) ?

The derivative of sqrt(2x-1/(x^2)) is (x^3+1)/(x^2sqrt(2x^3-1))

What is the first derivative of sqrt(2x-1/(x^2)) ?

The first derivative of sqrt(2x-1/(x^2)) is (x^3+1)/(x^2sqrt(2x^3-1))

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

\frac{x ^{3} + 1}{x ^{2} 2 x ^{3} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x ^{3} + 1}{x ^{2} 2 x ^{3} - 1}

\frac{d y}{d t}, y = e^{t}

\int sin^{5} (x) d x

\int sec^{2} (x) d x

\frac{d y}{d x} = \frac{y + 2}{x + 7}

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

What is the derivative of sqrt(2x-1/(x^2)) ?
The derivative of sqrt(2x-1/(x^2)) is (x^3+1)/(x^2sqrt(2x^3-1))
What is the first derivative of sqrt(2x-1/(x^2)) ?
The first derivative of sqrt(2x-1/(x^2)) is (x^3+1)/(x^2sqrt(2x^3-1))