What is the derivative of 1/(1-2/x) ?

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

What is the first derivative of 1/(1-2/x) ?

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

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d t} (cos (8 t))

y^{^{'}} = \frac{1}{( t \cdot y + y + t + 1 )}, y (0) = - 1

f (x) = x + 35, (1, 6)

\frac{d y}{d x} + x^{- 1} y = x y^{2}

e^{- t} cos (4 t)

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