What is the derivative of (3x+2/(5x-1)) ?

The derivative of (3x+2/(5x-1)) is -(13)/((5x-1)^2)

What is the first derivative of (3x+2/(5x-1)) ?

The first derivative of (3x+2/(5x-1)) is -(13)/((5x-1)^2)

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\frac{d}{d x} (\frac{3 x + 2}{5 x - 1})

- \frac{13}{( 5 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x + 2}{5 x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 2 ) ( 5 x - 1 ) - \frac{d}{d x} ( 5 x - 1 ) ( 3 x + 2 )}{( 5 x - 1 ) ^{2}}

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

\frac{d}{d x} (5 x - 1) = 5

= \frac{3 ( 5 x - 1 ) - 5 ( 3 x + 2 )}{( 5 x - 1 ) ^{2}}

Simplify

\frac{3 ( 5 x - 1 ) - 5 ( 3 x + 2 )}{( 5 x - 1 ) ^{2}} : - \frac{13}{( 5 x - 1 ) ^{2}}

= - \frac{13}{( 5 x - 1 ) ^{2}}

What is the derivative of (3x+2/(5x-1)) ?
The derivative of (3x+2/(5x-1)) is -(13)/((5x-1)^2)
What is the first derivative of (3x+2/(5x-1)) ?
The first derivative of (3x+2/(5x-1)) is -(13)/((5x-1)^2)