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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d j} (3 i - 4 j)

\frac{d h}{d t} = - h^{2}

\int \frac{1}{x ^{2} x ^{2} - 5} d x

y = x^{8 c o s (x)}

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

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