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)

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

- \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}}

Simplify

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

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

\int \frac{1}{t ^{\frac{3}{2}}} d t

\int \frac{2}{1 + 4 x ^{2}} d x

\int sin (\frac{1}{2})

z^{3}

\frac{\partial}{\partial x} (- x^{2} y^{2} z + 2 x y^{2} z^{2})

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)