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Popular >

derivative of (2+x/(x-1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x - 1 ) - 1 \cdot ( 2 + x )}{( x - 1 ) ^{2}} : - \frac{3}{( x - 1 ) ^{2}}

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (2+x/(x-1)) ?
The derivative of (2+x/(x-1)) is -3/((x-1)^2)
What is the first derivative of (2+x/(x-1)) ?
The first derivative of (2+x/(x-1)) is -3/((x-1)^2)