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Popular >

derivative of (2x-1)/(2x+3)

Solution

derivative of

\frac{2 x - 1}{2 x + 3}

Solution

\frac{8}{( 2 x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x - 1}{2 x + 3})

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

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

\frac{d}{d x} (2 x + 3) = 2

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

Expand

2 (2 x + 3) - 2 (2 x - 1) : 8

= \frac{8}{( 2 x + 3 ) ^{2}}

Popular Examples

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\int \frac{x ^{4} + 1}{x ^{3} - x ^{2}} d x

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\int_{7}^{9} \frac{y}{y ^{2} - 3 y - 4} d y

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\int (9 + u + u^{2}) d u

Frequently Asked Questions (FAQ)

What is the derivative of (2x-1)/(2x+3) ?
The derivative of (2x-1)/(2x+3) is 8/((2x+3)^2)
What is the first derivative of (2x-1)/(2x+3) ?
The first derivative of (2x-1)/(2x+3) is 8/((2x+3)^2)