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}}

im pl i c i t 7 x^{2} - y^{2} = 4

a re a y = x^{3}, y = 8, x = - 1

\frac{d}{d x} (\frac{5}{( 6 x + 5 ) ^{2}})

\int_{0}^{8} \frac{1}{64 - t ^{2}} d t

\frac{d}{d x} (cos^{2} (4 π x))

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)