What is the derivative of ((-4x(2x-2))/(-3x^2+1)) ?

The derivative of ((-4x(2x-2))/(-3x^2+1)) is -(4(-6x^2+4x-2))/((-3x^2+1)^2)

What is the first derivative of ((-4x(2x-2))/(-3x^2+1)) ?

The first derivative of ((-4x(2x-2))/(-3x^2+1)) is -(4(-6x^2+4x-2))/((-3x^2+1)^2)

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

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

Solution steps

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

Simplify

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

= \frac{d}{d x} (- \frac{4 x ( 2 x - 2 )}{- 3 x ^{2} + 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 4 \frac{d}{d x} (\frac{x ( 2 x - 2 )}{- 3 x ^{2} + 1})

Apply the Quotient Rule:

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

= - 4 \cdot \frac{\frac{d}{d x} ( x ( 2 x - 2 ) ) ( - 3 x ^{2} + 1 ) - \frac{d}{d x} ( - 3 x ^{2} + 1 ) x ( 2 x - 2 )}{( - 3 x ^{2} + 1 ) ^{2}}

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

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

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

Simplify

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

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

What is the derivative of ((-4x(2x-2))/(-3x^2+1)) ?
The derivative of ((-4x(2x-2))/(-3x^2+1)) is -(4(-6x^2+4x-2))/((-3x^2+1)^2)
What is the first derivative of ((-4x(2x-2))/(-3x^2+1)) ?
The first derivative of ((-4x(2x-2))/(-3x^2+1)) is -(4(-6x^2+4x-2))/((-3x^2+1)^2)