What is the derivative of (2x-3/(4x+1)) ?

The derivative of (2x-3/(4x+1)) is (14)/((4x+1)^2)

What is the first derivative of (2x-3/(4x+1)) ?

The first derivative of (2x-3/(4x+1)) is (14)/((4x+1)^2)

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\frac{d}{d x} (\frac{2 x - 3}{4 x + 1})

\frac{14}{( 4 x + 1 ) ^{2}}

Solution steps

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

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

\frac{d}{d x} (4 x + 1) = 4

= \frac{2 ( 4 x + 1 ) - 4 ( 2 x - 3 )}{( 4 x + 1 ) ^{2}}

Expand

2 (4 x + 1) - 4 (2 x - 3) : 14

= \frac{14}{( 4 x + 1 ) ^{2}}

What is the derivative of (2x-3/(4x+1)) ?
The derivative of (2x-3/(4x+1)) is (14)/((4x+1)^2)
What is the first derivative of (2x-3/(4x+1)) ?
The first derivative of (2x-3/(4x+1)) is (14)/((4x+1)^2)