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

The derivative of (2x^2-2x+2/((2x-1)^2)) is -6/((2x-1)^3)

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

The first derivative of (2x^2-2x+2/((2x-1)^2)) is -6/((2x-1)^3)

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

- \frac{6}{( 2 x - 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 4 x - 2 ) ( 2 x - 1 ) ^{2} - 4 ( 2 x - 1 ) ( 2 x ^{2} - 2 x + 2 )}{( ( 2 x - 1 ) ^{2} ) ^{2}} : - \frac{6}{( 2 x - 1 ) ^{3}}

= - \frac{6}{( 2 x - 1 ) ^{3}}

(4.5) (9.25)

x \to - \infty lim (\frac{5}{x})

\int (14 x + 2) d x

e ln (2 x^{4} + a x^{2} y^{2} + 2 y^{4})

y^{^{''}} - 9 y = (x^{2} - 2) sin (3 x)

What is the derivative of (2x^2-2x+2/((2x-1)^2)) ?
The derivative of (2x^2-2x+2/((2x-1)^2)) is -6/((2x-1)^3)
What is the first derivative of (2x^2-2x+2/((2x-1)^2)) ?
The first derivative of (2x^2-2x+2/((2x-1)^2)) is -6/((2x-1)^3)