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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Popular Examples

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\frac{d}{d x} (\frac{y}{x})

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\frac{d}{d x} (arcsin (\frac{a x}{4}))

(\partial)/(\partial y)(-5e^xcos(yz))

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\int \frac{a}{2} x + \frac{a}{2} d x

limit as x approaches 8 of 2x-7x^2

x \to 8 lim (2 x - 7 x^{2})

Frequently Asked Questions (FAQ)

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