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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

x^{2} - 6 x + 3

f (x) = ln (x^{2} - 3 x + 1), (3, 0)

\int_{- 5}^{0} (\frac{y}{5} + y + 6) d y

\frac{d y}{d x}, x y = 84

x \to 2 lim (2 x^{2} + 5 x + 2)

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