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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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