What is the derivative of (x^2-x+5/(4x-1)) ?

The derivative of (x^2-x+5/(4x-1)) is (4x^2-2x-19)/((4x-1)^2)

What is the first derivative of (x^2-x+5/(4x-1)) ?

The first derivative of (x^2-x+5/(4x-1)) is (4x^2-2x-19)/((4x-1)^2)

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\frac{d}{d x} (\frac{x ^{2} - x + 5}{4 x - 1})

\frac{4 x ^{2} - 2 x - 19}{( 4 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - x + 5}{4 x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - x + 5 ) ( 4 x - 1 ) - \frac{d}{d x} ( 4 x - 1 ) ( x ^{2} - x + 5 )}{( 4 x - 1 ) ^{2}}

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

\frac{d}{d x} (4 x - 1) = 4

= \frac{( 2 x - 1 ) ( 4 x - 1 ) - 4 ( x ^{2} - x + 5 )}{( 4 x - 1 ) ^{2}}

Expand

(2 x - 1) (4 x - 1) - 4 (x^{2} - x + 5) : 4 x^{2} - 2 x - 19

= \frac{4 x ^{2} - 2 x - 19}{( 4 x - 1 ) ^{2}}

What is the derivative of (x^2-x+5/(4x-1)) ?
The derivative of (x^2-x+5/(4x-1)) is (4x^2-2x-19)/((4x-1)^2)
What is the first derivative of (x^2-x+5/(4x-1)) ?
The first derivative of (x^2-x+5/(4x-1)) is (4x^2-2x-19)/((4x-1)^2)