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Popular Calculus >

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

Solution

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

Solution

- \frac{4}{( 2 x - 1 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{2 ( 2 x - 1 ) - 2 ( 2 x + 1 )}{( 2 x - 1 ) ^{2}} : - \frac{4}{( 2 x - 1 ) ^{2}}

= - \frac{4}{( 2 x - 1 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (2x+1/(2x-1)) ?
The derivative of (2x+1/(2x-1)) is -4/((2x-1)^2)
What is the first derivative of (2x+1/(2x-1)) ?
The first derivative of (2x+1/(2x-1)) is -4/((2x-1)^2)