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

The derivative of ((3x-1)/(2x+1)) is 5/((2x+1)^2)

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

The first derivative of ((3x-1)/(2x+1)) is 5/((2x+1)^2)

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

\frac{5}{( 2 x + 1 ) ^{2}}

Solution steps

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

\frac{d}{d x} (3 x - 1) = 3

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

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

Expand

3 (2 x + 1) - 2 (3 x - 1) : 5

= \frac{5}{( 2 x + 1 ) ^{2}}

What is the derivative of ((3x-1)/(2x+1)) ?
The derivative of ((3x-1)/(2x+1)) is 5/((2x+1)^2)
What is the first derivative of ((3x-1)/(2x+1)) ?
The first derivative of ((3x-1)/(2x+1)) is 5/((2x+1)^2)