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

The derivative of (1-x^{-2}) is 2/((1-x)^3)

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

The first derivative of (1-x^{-2}) is 2/((1-x)^3)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

y^{^{'}} = \frac{y}{x} + 1

y^{^{'''}} + 2 y^{^{''}} - 5 y^{^{'}} - 6 y = 0

\int_{0}^{π} 16 sin (x) d x

y^{^{''}} - y^{^{'}} + 20 y = 0

x \to 3 + lim (\frac{5}{x - 3})

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