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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Expand

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

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

2 x^{2} + 9

2 x^{2} + 2

sin^{- 2} (x)

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

\frac{d}{d t} (2 cos (12 t))

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