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

The derivative of (x+2/(x-1)) is -3/((x-1)^2)

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

3 x^{2} y + \frac{d y}{d x} = 4 x^{2}

n = 0 \sum \infty 3.2 5^{n}

f (x) = \frac{1}{3 + 2 x}, at x = 1

\int (4 x + 2) d x

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