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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

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