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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

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Frequently Asked Questions (FAQ)

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