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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (ln (\frac{x}{3}) + x^{2} - 8)

\frac{2}{3} t^{3} e^{- 8 t}

\frac{d}{d x} (3 cos (x) - sin (x))

\frac{d y}{d x} + 2 x y - y = 0, y (0) = 4

\int \frac{x + 9}{16 - ( x - 4 ) ^{2}} d x

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