What is the derivative of ((3x-2(2x-3))/(-2x^2+4x)) ?

The derivative of ((3x-2(2x-3))/(-2x^2+4x)) is -(x^2-12x+12)/(2x^2(x-2)^2)

What is the first derivative of ((3x-2(2x-3))/(-2x^2+4x)) ?

The first derivative of ((3x-2(2x-3))/(-2x^2+4x)) is -(x^2-12x+12)/(2x^2(x-2)^2)

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\frac{d}{d x} (\frac{( 3 x - 2 ) ( 2 x - 3 )}{- 2 x ^{2} + 4 x})

- \frac{x ^{2} - 12 x + 12}{2 x ^{2} ( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 3 x - 2 ) ( 2 x - 3 )}{- 2 x ^{2} + 4 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( 3 x - 2 ) ( 2 x - 3 ) ) ( - 2 x ^{2} + 4 x ) - \frac{d}{d x} ( - 2 x ^{2} + 4 x ) ( 3 x - 2 ) ( 2 x - 3 )}{( - 2 x ^{2} + 4 x ) ^{2}}

\frac{d}{d x} ((3 x - 2) (2 x - 3)) = 12 x - 13

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

= \frac{( 12 x - 13 ) ( - 2 x ^{2} + 4 x ) - ( - 4 x + 4 ) ( 3 x - 2 ) ( 2 x - 3 )}{( - 2 x ^{2} + 4 x ) ^{2}}

Simplify

\frac{( 12 x - 13 ) ( - 2 x ^{2} + 4 x ) - ( - 4 x + 4 ) ( 3 x - 2 ) ( 2 x - 3 )}{( - 2 x ^{2} + 4 x ) ^{2}} : - \frac{x ^{2} - 12 x + 12}{2 x ^{2} ( x - 2 ) ^{2}}

= - \frac{x ^{2} - 12 x + 12}{2 x ^{2} ( x - 2 ) ^{2}}

x y^{^{'}} + (1 + 2 x) y = 10 e^{- 2 x}

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

\int_{0}^{6} \frac{1}{36 + x ^{2}} d x

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

\frac{\partial}{\partial x} (10 x^{0.5})

What is the derivative of ((3x-2(2x-3))/(-2x^2+4x)) ?
The derivative of ((3x-2(2x-3))/(-2x^2+4x)) is -(x^2-12x+12)/(2x^2(x-2)^2)
What is the first derivative of ((3x-2(2x-3))/(-2x^2+4x)) ?
The first derivative of ((3x-2(2x-3))/(-2x^2+4x)) is -(x^2-12x+12)/(2x^2(x-2)^2)