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

The derivative of (1-3x-x^2/(x^2-4)) is (3x^2+6x+12)/((x^2-4)^2)

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

The first derivative of (1-3x-x^2/(x^2-4)) is (3x^2+6x+12)/((x^2-4)^2)

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

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

Solution steps

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

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

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

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

Expand

(- 2 x - 3) (x^{2} - 4) - 2 x (1 - 3 x - x^{2}) : 3 x^{2} + 6 x + 12

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

\frac{\partial}{\partial x} (\frac{x}{x ^{5} - y ^{7}})

e^{- 2 a x}

\frac{d}{d x} (e^{- 13 x})

\int \frac{cos ( ln ( x ) )}{x} d x

\frac{d}{d x} (e^{a t})

What is the derivative of (1-3x-x^2/(x^2-4)) ?
The derivative of (1-3x-x^2/(x^2-4)) is (3x^2+6x+12)/((x^2-4)^2)
What is the first derivative of (1-3x-x^2/(x^2-4)) ?
The first derivative of (1-3x-x^2/(x^2-4)) is (3x^2+6x+12)/((x^2-4)^2)