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

The derivative of ((3x^2-6)(x^2-2))/(x^2+4) is (6x^5+48x^3-120x)/((x^2+4)^2)

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

The first derivative of ((3x^2-6)(x^2-2))/(x^2+4) is (6x^5+48x^3-120x)/((x^2+4)^2)

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derivative of

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

\frac{6 x ^{5} + 48 x ^{3} - 120 x}{( x ^{2} + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((3 x^{2} - 6) (x^{2} - 2)) = 12 x^{3} - 24 x

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

= \frac{( 12 x ^{3} - 24 x ) ( x ^{2} + 4 ) - 2 x ( 3 x ^{2} - 6 ) ( x ^{2} - 2 )}{( x ^{2} + 4 ) ^{2}}

Expand

(12 x^{3} - 24 x) (x^{2} + 4) - 2 x (3 x^{2} - 6) (x^{2} - 2) : 6 x^{5} + 48 x^{3} - 120 x

= \frac{6 x ^{5} + 48 x ^{3} - 120 x}{( x ^{2} + 4 ) ^{2}}

\frac{\partial}{\partial x} (2 y)

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

x \to \infty lim (g (x))

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

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

What is the derivative of ((3x^2-6)(x^2-2))/(x^2+4) ?
The derivative of ((3x^2-6)(x^2-2))/(x^2+4) is (6x^5+48x^3-120x)/((x^2+4)^2)
What is the first derivative of ((3x^2-6)(x^2-2))/(x^2+4) ?
The first derivative of ((3x^2-6)(x^2-2))/(x^2+4) is (6x^5+48x^3-120x)/((x^2+4)^2)