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Popular >

derivative of (2x-5/(3x-1))

Solution

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

Solution

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

Solution steps

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

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

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

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

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

Expand

2 (3 x - 1) - 3 (2 x - 5) : 13

= \frac{13}{( 3 x - 1 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

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