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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\frac{d}{d x} (\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}}

x \to - 2 lim ((x + 1)^{5} (5 x^{2}))

\int 3 - 2 x d x

\frac{d}{d θ} (10 sin (θ))

\frac{d}{d x} (ln (\frac{3 e ^{x}}{2 x ^{2}}))

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)