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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

y = \frac{x}{1 + x ^{2}}, (2, 0.4)

\frac{d y}{d x} = \frac{x ^{2} y ^{3}}{x + 3}

x \to 4 + lim (\frac{4 - x}{∣ 4 - x ∣})

\frac{d}{d x} (- 5 x e^{x})

e^{5 t s i n (2 t)}

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