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

The derivative of (2x+3)/(3x-2) is -(13)/((3x-2)^2)

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

The first derivative of (2x+3)/(3x-2) is -(13)/((3x-2)^2)

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derivative of

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

- \frac{13}{( 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{13}{( 3 x - 2 ) ^{2}}

= - \frac{13}{( 3 x - 2 ) ^{2}}

\int (3 2 x + 1) d x

h \to + 0 lim (- \frac{5 h}{x ( x + h )})

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

\int \frac{6000}{6 x + 70} d x

\int \frac{3}{16 - 9 x ^{2}} d x

What is the derivative of (2x+3)/(3x-2) ?
The derivative of (2x+3)/(3x-2) is -(13)/((3x-2)^2)
What is the first derivative of (2x+3)/(3x-2) ?
The first derivative of (2x+3)/(3x-2) is -(13)/((3x-2)^2)