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

The derivative of (2x+5/(3x-2)) is -(19)/((3x-2)^2)

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

The first derivative of (2x+5/(3x-2)) is -(19)/((3x-2)^2)

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

- \frac{19}{( 3 x - 2 ) ^{2}}

Solution steps

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

\frac{d}{d x} (2 x + 5) = 2

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

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

Simplify

\frac{2 ( 3 x - 2 ) - 3 ( 2 x + 5 )}{( 3 x - 2 ) ^{2}} : - \frac{19}{( 3 x - 2 ) ^{2}}

= - \frac{19}{( 3 x - 2 ) ^{2}}

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

\frac{\partial}{\partial x} (sin (- 3 x) cos (4 y))

\frac{d}{d x} (x^{3} - 6 x^{2} + 11 x - 6)

\int 1 - y^{2} d y

What is the derivative of (2x+5/(3x-2)) ?
The derivative of (2x+5/(3x-2)) is -(19)/((3x-2)^2)
What is the first derivative of (2x+5/(3x-2)) ?
The first derivative of (2x+5/(3x-2)) is -(19)/((3x-2)^2)