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

The derivative of (2-2x-x^2/(x^2-4)) is (2x^2+4x+8)/((x^2-4)^2)

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

The first derivative of (2-2x-x^2/(x^2-4)) is (2x^2+4x+8)/((x^2-4)^2)

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

\frac{2 x ^{2} + 4 x + 8}{( x ^{2} - 4 ) ^{2}}

Solution steps

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

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

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

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

Expand

(- 2 x - 2) (x^{2} - 4) - 2 x (2 - 2 x - x^{2}) : 2 x^{2} + 4 x + 8

= \frac{2 x ^{2} + 4 x + 8}{( x ^{2} - 4 ) ^{2}}

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

\frac{d}{d x} (\frac{- 7 sin ( x )}{4 cos ( x )})

f (x) = 3 x^{4} (x^{2} - 4 x)

x \to 3 lim (\frac{∣ 3 - x ∣}{3 - x})

\int \frac{x ^{2}}{x + 15} d x

What is the derivative of (2-2x-x^2/(x^2-4)) ?
The derivative of (2-2x-x^2/(x^2-4)) is (2x^2+4x+8)/((x^2-4)^2)
What is the first derivative of (2-2x-x^2/(x^2-4)) ?
The first derivative of (2-2x-x^2/(x^2-4)) is (2x^2+4x+8)/((x^2-4)^2)