What is the derivative of (4x-5)/(3x+2) ?

The derivative of (4x-5)/(3x+2) is (23)/((3x+2)^2)

What is the first derivative of (4x-5)/(3x+2) ?

The first derivative of (4x-5)/(3x+2) is (23)/((3x+2)^2)

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derivative of

\frac{4 x - 5}{3 x + 2}

\frac{23}{( 3 x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - 5}{3 x + 2})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 4 x - 5 ) ( 3 x + 2 ) - \frac{d}{d x} ( 3 x + 2 ) ( 4 x - 5 )}{( 3 x + 2 ) ^{2}}

\frac{d}{d x} (4 x - 5) = 4

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

= \frac{4 ( 3 x + 2 ) - 3 ( 4 x - 5 )}{( 3 x + 2 ) ^{2}}

Expand

4 (3 x + 2) - 3 (4 x - 5) : 23

= \frac{23}{( 3 x + 2 ) ^{2}}

What is the derivative of (4x-5)/(3x+2) ?
The derivative of (4x-5)/(3x+2) is (23)/((3x+2)^2)
What is the first derivative of (4x-5)/(3x+2) ?
The first derivative of (4x-5)/(3x+2) is (23)/((3x+2)^2)